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                           <rdf:li><rdf:Description xmpDM:name="Mean of Ratios (Cont) If the numerator and the denominator are expected to follow a multiplicative property such that ai=c" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="bi, where c is approximately a constant that is being estimated, then c can be estimated by the geometric mean" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="of ai/bi." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example: Program Optimizer: Where, bi and ai are the sizes before and after the program optimization and c is the" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="effect of the optimization which is expected to be independent of the code size." xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= arithmetic mean of Þ c geometric mean of 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xmpDM:startTime="217233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Dispersion Range: Minimum and maximum of the values observed Variance or standard deviation 10- and 90- percentiles Semi" xmpDM:startTime="333533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="inter-quantile range Mean absolute deviation" xmpDM:startTime="333533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Range Range = Max-Min Larger range Þ higher variability In most cases, range is not very useful." xmpDM:startTime="354633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The minimum often comes out to be zero and the maximum comes out to be an ``outlier'' far from typical" xmpDM:startTime="354633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="values." xmpDM:startTime="354633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Unless the variable is bounded, the maximum 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minimum and maximum." xmpDM:startTime="1053367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It can be done for any variable, even for variables without bounds." xmpDM:startTime="1053367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="When expressed as a fraction between 0 and 1 (instead of a percent), the percentiles are also called quantiles." xmpDM:startTime="1053367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 0.9-quantile" xmpDM:startTime="1053367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is the same as 90-percentile." xmpDM:startTime="1053367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fractile= quantile." xmpDM:startTime="1053367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The percentiles at multiples of 10% are called deciles." xmpDM:startTime="1053367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Thus, the first decile is 10-percentile, the second decile is 20-percentile, and so on." xmpDM:startTime="1053367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1053367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quartiles Quartiles divide the data into four parts at 25%, 50%, and 75%." xmpDM:startTime="1150100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 25% of the observations are less than or equal to the first quartile Q1, 50% of the observations are" xmpDM:startTime="1150100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="less than or equal to the second quartile Q2, and 75% are less than or equal to the third quartile" xmpDM:startTime="1150100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Q3." xmpDM:startTime="1150100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Notice that the second quartile Q2 is also the median." xmpDM:startTime="1150100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The a-quantiles can be estimated by sorting the observations and taking the [(n-1)a+1]th element in the ordered set." xmpDM:startTime="1150100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Here, [.]" xmpDM:startTime="1150100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used to denote rounding to the nearest integer." xmpDM:startTime="1150100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="To be precise, use linear interpolation for continuous variables." xmpDM:startTime="1150100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1150100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi Inter-Quartile Range Inter-quartile range = Q_3- Q_1 Semi inter-quartile range (SIQR) TP_tmp" xmpDM:startTime="1244933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean Absolute Deviation No multiplication or square root is required TP_tmp" xmpDM:startTime="1256167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi Inter-Quartile Range Inter-quartile range = Q_3- Q_1 Semi inter-quartile range (SIQR) TP_tmp" xmpDM:startTime="1282000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quartiles Quartiles divide the data into four parts at 25%, 50%, and 75%." xmpDM:startTime="1282767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 25% of the observations are less than or equal to the first quartile Q1, 50% of the observations are" xmpDM:startTime="1282767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="less than or equal to the second quartile Q2, and 75% are less than or equal to the third quartile" xmpDM:startTime="1282767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Q3." xmpDM:startTime="1282767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Notice that the second quartile Q2 is also the median." xmpDM:startTime="1282767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The a-quantiles can be estimated by sorting the observations and taking the [(n-1)a+1]th element in the ordered set." xmpDM:startTime="1282767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Here, [.]" xmpDM:startTime="1282767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used to denote rounding to the nearest integer." xmpDM:startTime="1282767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="To be precise, use linear interpolation for continuous variables." xmpDM:startTime="1282767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1282767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi Inter-Quartile Range Inter-quartile range = Q_3- Q_1 Semi inter-quartile range (SIQR) TP_tmp" xmpDM:startTime="1323767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quartiles Quartiles divide the data into four parts at 25%, 50%, and 75%." xmpDM:startTime="1324967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 25% of the observations are less than or equal to the first quartile Q1, 50% of the observations are" xmpDM:startTime="1324967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="less than or equal to the second quartile Q2, and 75% are less than or equal to the third quartile" xmpDM:startTime="1324967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Q3." xmpDM:startTime="1324967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Notice that the second quartile Q2 is also the median." xmpDM:startTime="1324967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The a-quantiles can be estimated by sorting the observations and taking the [(n-1)a+1]th element in the ordered set." xmpDM:startTime="1324967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Here, [.]" xmpDM:startTime="1324967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used to denote rounding to the nearest integer." xmpDM:startTime="1324967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="To be precise, use linear interpolation for continuous variables." xmpDM:startTime="1324967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1324967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi Inter-Quartile Range Inter-quartile range = Q_3- Q_1 Semi inter-quartile range (SIQR) TP_tmp" xmpDM:startTime="1518900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean Absolute Deviation No multiplication or square root is required TP_tmp" xmpDM:startTime="1543733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi Inter-Quartile Range Inter-quartile range = Q_3- Q_1 Semi inter-quartile range (SIQR) TP_tmp" xmpDM:startTime="1556067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean Absolute Deviation No multiplication or square root is required TP_tmp" xmpDM:startTime="1567600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Comparison of Variation Measures Range is affected considerably by outliers." xmpDM:startTime="1625233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Sample variance is also affected by outliers but the affect is less Mean absolute deviation is next in resistance to" xmpDM:startTime="1625233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="outliers." xmpDM:startTime="1625233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi inter-quantile range is very resistant to outliers." xmpDM:startTime="1625233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="If the distribution is highly skewed, outliers are highly likely and SIQR is preferred over standard deviation In general, SIQR" xmpDM:startTime="1625233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used as an index of dispersion whenever median is used as an index of central tendency." xmpDM:startTime="1625233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For qualitative (categorical) data, the dispersion can be specified by giving the number of most frequent categories that comprise the" xmpDM:startTime="1625233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="given percentile, for instance, top 90%." xmpDM:startTime="1625233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1625233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean 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xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Notice that the second quartile Q2 is also the median." xmpDM:startTime="1627233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The a-quantiles can be estimated by sorting the observations and taking the [(n-1)a+1]th element in the ordered set." xmpDM:startTime="1627233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Here, [.]" xmpDM:startTime="1627233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used to denote rounding to the nearest integer." xmpDM:startTime="1627233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="To be precise, use linear interpolation for continuous variables." xmpDM:startTime="1627233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1627233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Percentiles Specifying the 5-percentile and the 95-percentile of a variable has the same impact as specifying its minimum and maximum." xmpDM:startTime="1627333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It can be done for any variable, even for variables without bounds." xmpDM:startTime="1627333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="When expressed as a fraction between 0 and 1 (instead of a percent), the percentiles are also called quantiles." xmpDM:startTime="1627333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 0.9-quantile" xmpDM:startTime="1627333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is the same as 90-percentile." xmpDM:startTime="1627333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fractile= quantile." xmpDM:startTime="1627333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The percentiles at multiples of 10% are called deciles." xmpDM:startTime="1627333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Thus, the first decile is 10-percentile, the second decile is 20-percentile, and so on." xmpDM:startTime="1627333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1627333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance (Cont) Variance is expressed in units which are square of the units of the observations." xmpDM:startTime="1627533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ It is preferable to use standard deviation." xmpDM:startTime="1627533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Ratio of standard deviation to the mean, or the coefficient of variance (COV), is even better because it takes the" xmpDM:startTime="1627533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="scale of measurement (unit of measurement) out of variability consideration." xmpDM:startTime="1627533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1627533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance The divisor for s2 is n-1 and not n." xmpDM:startTime="1628000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This is because only n-1 of the n differences are independent." xmpDM:startTime="1628000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Given n-1 differences, nth difference can be computed since the sum of all n differences must be zero." xmpDM:startTime="1628000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The number of independent terms in a sum is also called its degrees of freedom." xmpDM:startTime="1628000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp TP_tmp" xmpDM:startTime="1628000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Range Range = Max-Min Larger range Þ higher variability In most cases, range is not very useful." xmpDM:startTime="1628333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The minimum often comes out to be zero and the maximum comes out to be an ``outlier'' far from typical" xmpDM:startTime="1628333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="values." xmpDM:startTime="1628333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Unless the variable is bounded, the maximum goes on increasing with the number of observations, the minimum goes on decreasing" xmpDM:startTime="1628333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="with the number of observations, and there is no ``stable'' point that gives a good indication of the actual range." xmpDM:startTime="1628333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Range is useful if, and only if, there is a reason to believe that the variable is bounded." xmpDM:startTime="1628333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1628333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Dispersion Range: Minimum and maximum of the values observed Variance or standard deviation 10- and 90- percentiles Semi" xmpDM:startTime="1628833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="inter-quantile range Mean absolute deviation" xmpDM:startTime="1628833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Range Range = Max-Min Larger range Þ higher variability In most cases, range is not very useful." xmpDM:startTime="1655867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The minimum often comes out to be zero and the maximum comes out to be an ``outlier'' far from typical" xmpDM:startTime="1655867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="values." xmpDM:startTime="1655867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Unless the variable is bounded, the maximum goes on increasing with the number of observations, the minimum goes on decreasing" xmpDM:startTime="1655867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="with the number of observations, and there is no ``stable'' point that gives a good indication of the actual range." xmpDM:startTime="1655867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Range is useful if, and only if, there is a reason to believe that the variable is bounded." xmpDM:startTime="1655867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1655867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance The divisor for s2 is n-1 and not n." xmpDM:startTime="1656400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This is because only n-1 of the n differences are independent." xmpDM:startTime="1656400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Given n-1 differences, nth difference can be computed since the sum of all n differences must be zero." xmpDM:startTime="1656400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The number of independent terms in a sum is also called its degrees of freedom." xmpDM:startTime="1656400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp TP_tmp" xmpDM:startTime="1656400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance (Cont) Variance is expressed in units which are square of the units of the observations." xmpDM:startTime="1657000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ It is preferable to use standard deviation." xmpDM:startTime="1657000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Ratio of standard deviation to the mean, or the coefficient of variance (COV), is even better because it takes the" xmpDM:startTime="1657000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="scale of measurement (unit of measurement) out of variability consideration." xmpDM:startTime="1657000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1657000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Percentiles Specifying the 5-percentile and the 95-percentile of a variable has the same impact as specifying its minimum and maximum." xmpDM:startTime="1657500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It can be done for any variable, even for variables without bounds." xmpDM:startTime="1657500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="When expressed as a fraction between 0 and 1 (instead of a percent), the percentiles are also called quantiles." xmpDM:startTime="1657500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 0.9-quantile" xmpDM:startTime="1657500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is the same as 90-percentile." xmpDM:startTime="1657500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fractile= quantile." xmpDM:startTime="1657500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The percentiles at multiples of 10% are called deciles." xmpDM:startTime="1657500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Thus, the first decile is 10-percentile, the second decile is 20-percentile, and so on." xmpDM:startTime="1657500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1657500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quartiles Quartiles divide the data into four parts at 25%, 50%, and 75%." xmpDM:startTime="1657967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 25% of the observations are less than or equal to the first quartile Q1, 50% of the observations are" xmpDM:startTime="1657967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="less than or equal to the second quartile Q2, and 75% are less than or equal to the third quartile" xmpDM:startTime="1657967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Q3." xmpDM:startTime="1657967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Notice that the second quartile Q2 is also the median." xmpDM:startTime="1657967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The a-quantiles can be estimated by sorting the observations and taking the [(n-1)a+1]th element in the ordered set." xmpDM:startTime="1657967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Here, [.]" xmpDM:startTime="1657967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used to denote rounding to the nearest integer." xmpDM:startTime="1657967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="To be precise, use linear interpolation for continuous variables." xmpDM:startTime="1657967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1657967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi Inter-Quartile Range Inter-quartile range = Q_3- Q_1 Semi inter-quartile range (SIQR) TP_tmp" xmpDM:startTime="1658667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean Absolute Deviation No multiplication or square root is required TP_tmp" xmpDM:startTime="1659367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Comparison of Variation Measures Range is affected considerably by outliers." xmpDM:startTime="1660000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Sample variance is also affected by outliers but the affect is less Mean absolute deviation is next in resistance to" xmpDM:startTime="1660000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="outliers." xmpDM:startTime="1660000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi inter-quantile range is very resistant to outliers." xmpDM:startTime="1660000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="If the distribution is highly skewed, outliers are highly likely and SIQR is preferred over standard deviation In general, SIQR" xmpDM:startTime="1660000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used as an index of dispersion whenever median is used as an index of central tendency." xmpDM:startTime="1660000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For qualitative (categorical) data, the dispersion can be specified by giving the number of most frequent categories that comprise the" xmpDM:startTime="1660000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="given percentile, for instance, top 90%." xmpDM:startTime="1660000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1660000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Measures of Variation: Example In an experiment, which was repeated 32 times, the measured CPU time was found to be" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="{3.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.4," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.6," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.7," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.6," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.8," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.4," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.3," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.3," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.7," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.8," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2}." xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The sorted set is {1.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.7," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.3," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.4," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.6," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.7," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.8," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.4," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.8," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.9," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.3," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.6," xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.9}." xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="10-percentile = [ 1+(31)(0.10)]" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= [4.1]" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="=4th element = 2.8" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="90-percentile = [ 1+(31)(0.90)]" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= [28.9]" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 29th element = 5.1" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="First quartile Q1 = [1+(31)(0.25)]" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="=[8.875]=" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="9th element = 3.2" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Median Q2 = [ 1+(31)(0.50)]" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= [16.5]" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 0.5(16th" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="+17th elements) = 0.5(3.9+3.9)" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 3.9" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Third quartile Q3 = [ 1+(31)(0.75)]" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="=[24.25]" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 24th element = 4.5" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="1895700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting the Index of Dispersion chp_12_04-1" xmpDM:startTime="2070567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting the Index of Dispersion (Cont) The decision rules given above are not hard and fast." xmpDM:startTime="2118867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Network designed for average traffic is grossly under-designed." xmpDM:startTime="2118867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The network load is highly skewed Þ Networks are designed to carry 95 to 99-percentile of the observed load levels" xmpDM:startTime="2118867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ Dispersion of the load should be specified via range or percentiles." xmpDM:startTime="2118867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Power supplies are similarly designed to sustain peak demand rather than average demand." xmpDM:startTime="2118867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Finding a percentile requires several passes through the data, and therefore, the observations have to be stored." xmpDM:startTime="2118867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Heuristic algorithms, e.g.," xmpDM:startTime="2118867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="P2 allows dynamic calculation of percentiles as the observations are generated." xmpDM:startTime="2118867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="See Box 12.1" xmpDM:startTime="2118867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="in the book for a summary of formulas for various indices of central tendencies and dispersion" xmpDM:startTime="2118867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determining Distribution of Data The simplest way to determine the distribution is to plot a histogram Count observations that fall" xmpDM:startTime="2364700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="into each cell or bucket The key problem is determining the cell size." xmpDM:startTime="2364700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Small cells Þ large variation in the number of observations per cell Large cells Þ details of the distribution are" xmpDM:startTime="2364700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="completely lost." xmpDM:startTime="2364700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It is possible to reach very different conclusions about the distribution shape One guideline: if any cell has less than" xmpDM:startTime="2364700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="five observations, the cell size should be increased or a variable cell histogram should be used." xmpDM:startTime="2364700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2364700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting the Index of Dispersion (Cont) The decision rules given above are not hard and fast." xmpDM:startTime="2367300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Network designed for average traffic is grossly under-designed." xmpDM:startTime="2367300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The network load is highly skewed Þ Networks are designed to carry 95 to 99-percentile of the observed load levels" xmpDM:startTime="2367300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ Dispersion of the load should be specified via range or percentiles." xmpDM:startTime="2367300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Power supplies are similarly designed to sustain peak demand rather than average demand." xmpDM:startTime="2367300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Finding a percentile requires several passes through the data, and therefore, the observations have to be stored." xmpDM:startTime="2367300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Heuristic algorithms, e.g.," xmpDM:startTime="2367300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="P2 allows dynamic calculation of percentiles as the observations are generated." xmpDM:startTime="2367300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="See Box 12.1" xmpDM:startTime="2367300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="in the book for a summary of formulas for various indices of central tendencies and dispersion" xmpDM:startTime="2367300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting the Index of Dispersion chp_12_04-1" xmpDM:startTime="2406900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Measures of Variation: Example In an experiment, which was repeated 32 times, the measured CPU time was found to be" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="{3.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.4," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.6," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.7," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.6," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.8," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.4," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.3," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.3," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.7," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.8," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2}." xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The sorted set is {1.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.7," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.3," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.4," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.6," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.7," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.8," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.4," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.8," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.9," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.3," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.6," xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.9}." xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="10-percentile = [ 1+(31)(0.10)]" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= [4.1]" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="=4th element = 2.8" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="90-percentile = [ 1+(31)(0.90)]" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= [28.9]" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 29th element = 5.1" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="First quartile Q1 = [1+(31)(0.25)]" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="=[8.875]=" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="9th element = 3.2" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Median Q2 = [ 1+(31)(0.50)]" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= [16.5]" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 0.5(16th" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="+17th elements) = 0.5(3.9+3.9)" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 3.9" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Third quartile Q3 = [ 1+(31)(0.75)]" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="=[24.25]" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 24th element = 4.5" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="2407167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Comparison of Variation Measures Range is affected considerably by outliers." xmpDM:startTime="2407333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Sample variance is also affected by outliers but the affect is less Mean absolute deviation is next in resistance to" xmpDM:startTime="2407333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="outliers." xmpDM:startTime="2407333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi inter-quantile range is very resistant to outliers." xmpDM:startTime="2407333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="If the distribution is highly skewed, outliers are highly likely and SIQR is preferred over standard deviation In general, SIQR" xmpDM:startTime="2407333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used as an index of dispersion whenever median is used as an index of central tendency." xmpDM:startTime="2407333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For qualitative (categorical) data, the dispersion can be specified by giving the number of most frequent categories that comprise the" xmpDM:startTime="2407333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="given percentile, for instance, top 90%." xmpDM:startTime="2407333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2407333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean Absolute Deviation No multiplication or square root is required TP_tmp" xmpDM:startTime="2407500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi Inter-Quartile Range Inter-quartile range = Q_3- Q_1 Semi inter-quartile range (SIQR) TP_tmp" xmpDM:startTime="2407700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quartiles Quartiles divide the data into four parts at 25%, 50%, and 75%." xmpDM:startTime="2408633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 25% of the observations are less than or equal to the first quartile Q1, 50% of the observations are" xmpDM:startTime="2408633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="less than or equal to the second quartile Q2, and 75% are less than or equal to the third quartile" xmpDM:startTime="2408633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Q3." xmpDM:startTime="2408633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Notice that the second quartile Q2 is also the median." xmpDM:startTime="2408633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The a-quantiles can be estimated by sorting the observations and taking the [(n-1)a+1]th element in the ordered set." xmpDM:startTime="2408633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Here, [.]" xmpDM:startTime="2408633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used to denote rounding to the nearest integer." xmpDM:startTime="2408633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="To be precise, use linear interpolation for continuous variables." xmpDM:startTime="2408633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2408633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Percentiles Specifying the 5-percentile and the 95-percentile of a variable has the same impact as specifying its minimum and maximum." xmpDM:startTime="2409167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It can be done for any variable, even for variables without bounds." xmpDM:startTime="2409167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="When expressed as a fraction between 0 and 1 (instead of a percent), the percentiles are also called quantiles." xmpDM:startTime="2409167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 0.9-quantile" xmpDM:startTime="2409167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is the same as 90-percentile." xmpDM:startTime="2409167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fractile= quantile." xmpDM:startTime="2409167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The percentiles at multiples of 10% are called deciles." xmpDM:startTime="2409167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Thus, the first decile is 10-percentile, the second decile is 20-percentile, and so on." xmpDM:startTime="2409167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2409167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance (Cont) Variance is expressed in units which are square of the units of the observations." xmpDM:startTime="2409467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ It is preferable to use standard deviation." xmpDM:startTime="2409467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Ratio of standard deviation to the mean, or the coefficient of variance (COV), is even better because it takes the" xmpDM:startTime="2409467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="scale of measurement (unit of measurement) out of variability consideration." xmpDM:startTime="2409467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2409467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance The divisor for s2 is n-1 and not n." xmpDM:startTime="2409833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This is because only n-1 of the n differences are independent." xmpDM:startTime="2409833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Given n-1 differences, nth difference can be computed since the sum of all n differences must be zero." xmpDM:startTime="2409833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The number of independent terms in a sum is also called its degrees of freedom." xmpDM:startTime="2409833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp TP_tmp" xmpDM:startTime="2409833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Range Range = Max-Min Larger range Þ higher variability In most cases, range is not very useful." xmpDM:startTime="2410133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The minimum often comes out to be zero and the maximum comes out to be an ``outlier'' far from typical" xmpDM:startTime="2410133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="values." xmpDM:startTime="2410133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Unless the variable is bounded, the maximum goes on increasing with the number of observations, the minimum goes on decreasing" xmpDM:startTime="2410133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="with the number of observations, and there is no ``stable'' point that gives a good indication of the actual range." xmpDM:startTime="2410133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Range is useful if, and only if, there is a reason to believe that the variable is bounded." xmpDM:startTime="2410133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2410133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Dispersion Range: Minimum and maximum of the values observed Variance or standard deviation 10- and 90- percentiles Semi" xmpDM:startTime="2410600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="inter-quantile range Mean absolute deviation" xmpDM:startTime="2410600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summarizing Variability “Then there is the man who drowned crossing a stream with an average depth of six inches.”" xmpDM:startTime="2410967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="- W." xmpDM:startTime="2410967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="I." xmpDM:startTime="2410967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="E." xmpDM:startTime="2410967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Gates chp_12_03" xmpDM:startTime="2410967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Program Optimizer Static Size Data TP_tmp" xmpDM:startTime="2411633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean of Ratios (Cont) If the numerator and the denominator are expected to follow a multiplicative property such that ai=c" xmpDM:startTime="2536100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="bi, where c is approximately a constant that is being estimated, then c can be estimated by the geometric mean" xmpDM:startTime="2536100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="of ai/bi." xmpDM:startTime="2536100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example: Program Optimizer: Where, bi and ai are the sizes before and after the program optimization and c is the" xmpDM:startTime="2536100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="effect of the optimization which is expected to be independent of the code size." xmpDM:startTime="2536100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= arithmetic mean of Þ c geometric mean of ai/bi TP_tmp TP_tmp TP_tmp" xmpDM:startTime="2536100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Program Optimizer Static Size Data TP_tmp" xmpDM:startTime="2538900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean of Ratios (Cont) If the numerator and the denominator are expected to follow a multiplicative property such that ai=c" xmpDM:startTime="2619467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="bi, where c is approximately a constant that is being estimated, then c can be estimated by the geometric mean" xmpDM:startTime="2619467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="of ai/bi." xmpDM:startTime="2619467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example: Program Optimizer: Where, bi and ai are the sizes before and after the program optimization and c is the" xmpDM:startTime="2619467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="effect of the optimization which is expected to be independent of the code size." xmpDM:startTime="2619467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= arithmetic mean of Þ c geometric mean of ai/bi TP_tmp TP_tmp TP_tmp" xmpDM:startTime="2619467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Program Optimizer Static Size Data TP_tmp" xmpDM:startTime="2628433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summarizing Variability “Then there is the man who drowned crossing a stream with an average depth of six inches.”" xmpDM:startTime="2638167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="- W." xmpDM:startTime="2638167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="I." xmpDM:startTime="2638167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="E." xmpDM:startTime="2638167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Gates chp_12_03" xmpDM:startTime="2638167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Dispersion Range: Minimum and maximum of the values observed Variance or standard deviation 10- and 90- percentiles Semi" xmpDM:startTime="2638367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="inter-quantile range Mean absolute deviation" xmpDM:startTime="2638367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Range Range = Max-Min Larger range Þ higher variability In most cases, range is not very useful." xmpDM:startTime="2638533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The minimum often comes out to be zero and the maximum comes out to be an ``outlier'' far from typical" xmpDM:startTime="2638533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="values." xmpDM:startTime="2638533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Unless the variable is bounded, the maximum goes on increasing with the number of observations, the minimum goes on decreasing" xmpDM:startTime="2638533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="with the number of observations, and there is no ``stable'' point that gives a good indication of the actual range." xmpDM:startTime="2638533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Range is useful if, and only if, there is a reason to believe that the variable is bounded." xmpDM:startTime="2638533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2638533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance The divisor for s2 is n-1 and not n." xmpDM:startTime="2638667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This is because only n-1 of the n differences are independent." xmpDM:startTime="2638667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Given n-1 differences, nth difference can be computed since the sum of all n differences must be zero." xmpDM:startTime="2638667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The number of independent terms in a sum is also called its degrees of freedom." xmpDM:startTime="2638667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp TP_tmp" xmpDM:startTime="2638667" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Variance (Cont) Variance is expressed in units which are square of the units of the observations." xmpDM:startTime="2638867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ It is preferable to use standard deviation." xmpDM:startTime="2638867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Ratio of standard deviation to the mean, or the coefficient of variance (COV), is even better because it takes the" xmpDM:startTime="2638867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="scale of measurement (unit of measurement) out of variability consideration." xmpDM:startTime="2638867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2638867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Percentiles Specifying the 5-percentile and the 95-percentile of a variable has the same impact as specifying its minimum and maximum." xmpDM:startTime="2639033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It can be done for any variable, even for variables without bounds." xmpDM:startTime="2639033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="When expressed as a fraction between 0 and 1 (instead of a percent), the percentiles are also called quantiles." xmpDM:startTime="2639033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 0.9-quantile" xmpDM:startTime="2639033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is the same as 90-percentile." xmpDM:startTime="2639033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Fractile= quantile." xmpDM:startTime="2639033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The percentiles at multiples of 10% are called deciles." xmpDM:startTime="2639033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Thus, the first decile is 10-percentile, the second decile is 20-percentile, and so on." xmpDM:startTime="2639033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2639033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quartiles Quartiles divide the data into four parts at 25%, 50%, and 75%." xmpDM:startTime="2639333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ 25% of the observations are less than or equal to the first quartile Q1, 50% of the observations are" xmpDM:startTime="2639333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="less than or equal to the second quartile Q2, and 75% are less than or equal to the third quartile" xmpDM:startTime="2639333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Q3." xmpDM:startTime="2639333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Notice that the second quartile Q2 is also the median." xmpDM:startTime="2639333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The a-quantiles can be estimated by sorting the observations and taking the [(n-1)a+1]th element in the ordered set." xmpDM:startTime="2639333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Here, [.]" xmpDM:startTime="2639333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used to denote rounding to the nearest integer." xmpDM:startTime="2639333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="To be precise, use linear interpolation for continuous variables." xmpDM:startTime="2639333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2639333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi Inter-Quartile Range Inter-quartile range = Q_3- Q_1 Semi inter-quartile range (SIQR) TP_tmp" xmpDM:startTime="2639633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean Absolute Deviation No multiplication or square root is required TP_tmp" xmpDM:startTime="2639900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Comparison of Variation Measures Range is affected considerably by outliers." xmpDM:startTime="2640333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Sample variance is also affected by outliers but the affect is less Mean absolute deviation is next in resistance to" xmpDM:startTime="2640333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="outliers." xmpDM:startTime="2640333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Semi inter-quantile range is very resistant to outliers." xmpDM:startTime="2640333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="If the distribution is highly skewed, outliers are highly likely and SIQR is preferred over standard deviation In general, SIQR" xmpDM:startTime="2640333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is used as an index of dispersion whenever median is used as an index of central tendency." xmpDM:startTime="2640333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For qualitative (categorical) data, the dispersion can be specified by giving the number of most frequent categories that comprise the" xmpDM:startTime="2640333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="given percentile, for instance, top 90%." xmpDM:startTime="2640333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2640333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Measures of Variation: Example In an experiment, which was repeated 32 times, the measured CPU time was found to be" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="{3.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.4," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.6," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.7," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.6," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.8," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.4," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.3," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.3," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="1.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.7," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.8," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2}." xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The sorted set is {1.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.7," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.8," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="2.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.2," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.3," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.4," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.6," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.7," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.8," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="3.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.2," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.4," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.5," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.8," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="4.9," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.1," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.3," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.6," xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="5.9}." xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="10-percentile = [ 1+(31)(0.10)]" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= [4.1]" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="=4th element = 2.8" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="90-percentile = [ 1+(31)(0.90)]" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= [28.9]" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 29th element = 5.1" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="First quartile Q1 = [1+(31)(0.25)]" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="=[8.875]=" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="9th element = 3.2" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Median Q2 = [ 1+(31)(0.50)]" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= [16.5]" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 0.5(16th" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="+17th elements) = 0.5(3.9+3.9)" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 3.9" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Third quartile Q3 = [ 1+(31)(0.75)]" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="=[24.25]" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="= 24th element = 4.5" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="2640733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting the Index of Dispersion chp_12_04-1" xmpDM:startTime="2641067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting the Index of Dispersion (Cont) The decision rules given above are not hard and fast." xmpDM:startTime="2641733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Network designed for average traffic is grossly under-designed." xmpDM:startTime="2641733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The network load is highly skewed Þ Networks are designed to carry 95 to 99-percentile of the observed load levels" xmpDM:startTime="2641733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ Dispersion of the load should be specified via range or percentiles." xmpDM:startTime="2641733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Power supplies are similarly designed to sustain peak demand rather than average demand." xmpDM:startTime="2641733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Finding a percentile requires several passes through the data, and therefore, the observations have to be stored." xmpDM:startTime="2641733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Heuristic algorithms, e.g.," xmpDM:startTime="2641733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="P2 allows dynamic calculation of percentiles as the observations are generated." xmpDM:startTime="2641733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="See Box 12.1" xmpDM:startTime="2641733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="in the book for a summary of formulas for various indices of central tendencies and dispersion" xmpDM:startTime="2641733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determining Distribution of Data The simplest way to determine the distribution is to plot a histogram Count observations that fall" xmpDM:startTime="2642133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="into each cell or bucket The key problem is determining the cell size." xmpDM:startTime="2642133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Small cells Þ large variation in the number of observations per cell Large cells Þ details of the distribution are" xmpDM:startTime="2642133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="completely lost." xmpDM:startTime="2642133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It is possible to reach very different conclusions about the distribution shape One guideline: if any cell has less than" xmpDM:startTime="2642133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="five observations, the cell size should be increased or a variable cell histogram should be used." xmpDM:startTime="2642133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2642133" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile plots y(i) is the observed qith quantile xi = theoretical qith quantile (xi, y(i)) plot should be a straight" xmpDM:startTime="2672433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="line To determine the qith quantile xi, need to invert the cumulative distribution function." xmpDM:startTime="2672433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="or Table 28.1" xmpDM:startTime="2672433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="lists the inverse of CDF for a number of distributions." xmpDM:startTime="2672433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp" xmpDM:startTime="2672433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile plots (Cont) Approximation for normal distribution N(0,1) For N(m, s), the xi values computed above are scaled to m+s" xmpDM:startTime="2672967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="xi before plotting." xmpDM:startTime="2672967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="2672967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile plots y(i) is the observed qith quantile xi = theoretical qith quantile (xi, y(i)) plot should be a straight" xmpDM:startTime="2673933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="line To determine the qith quantile xi, need to invert the cumulative distribution function." xmpDM:startTime="2673933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="or Table 28.1" xmpDM:startTime="2673933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="lists the inverse of CDF for a number of distributions." xmpDM:startTime="2673933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp" xmpDM:startTime="2673933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determining Distribution of Data The simplest way to determine the distribution is to plot a histogram Count observations that fall" xmpDM:startTime="2674233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="into each cell or bucket The key problem is determining the cell size." xmpDM:startTime="2674233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Small cells Þ large variation in the number of observations per cell Large cells Þ details of the distribution are" xmpDM:startTime="2674233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="completely lost." xmpDM:startTime="2674233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It is possible to reach very different conclusions about the distribution shape One guideline: if any cell has less than" xmpDM:startTime="2674233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="five observations, the cell size should be increased or a variable cell histogram should be used." xmpDM:startTime="2674233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2674233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting the Index of Dispersion (Cont) The decision rules given above are not hard and fast." xmpDM:startTime="2674500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Network designed for average traffic is grossly under-designed." xmpDM:startTime="2674500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The network load is highly skewed Þ Networks are designed to carry 95 to 99-percentile of the observed load levels" xmpDM:startTime="2674500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Þ Dispersion of the load should be specified via range or percentiles." xmpDM:startTime="2674500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Power supplies are similarly designed to sustain peak demand rather than average demand." xmpDM:startTime="2674500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Finding a percentile requires several passes through the data, and therefore, the observations have to be stored." xmpDM:startTime="2674500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Heuristic algorithms, e.g.," xmpDM:startTime="2674500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="P2 allows dynamic calculation of percentiles as the observations are generated." xmpDM:startTime="2674500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="See Box 12.1" xmpDM:startTime="2674500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="in the book for a summary of formulas for various indices of central tendencies and dispersion" xmpDM:startTime="2674500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determining Distribution of Data The simplest way to determine the distribution is to plot a histogram Count observations that fall" xmpDM:startTime="2675833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="into each cell or bucket The key problem is determining the cell size." xmpDM:startTime="2675833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Small cells Þ large variation in the number of observations per cell Large cells Þ details of the distribution are" xmpDM:startTime="2675833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="completely lost." xmpDM:startTime="2675833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It is possible to reach very different conclusions about the distribution shape One guideline: if any cell has less than" xmpDM:startTime="2675833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="five observations, the cell size should be increased or a variable cell histogram should be used." xmpDM:startTime="2675833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2675833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile plots y(i) is the observed qith quantile xi = theoretical qith quantile (xi, y(i)) plot should be a straight" xmpDM:startTime="2741767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="line To determine the qith quantile xi, need to invert the cumulative distribution function." xmpDM:startTime="2741767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="or Table 28.1" xmpDM:startTime="2741767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="lists the inverse of CDF for a number of distributions." xmpDM:startTime="2741767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp" xmpDM:startTime="2741767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile plots (Cont) Approximation for normal distribution N(0,1) For N(m, s), the xi values computed above are scaled to m+s" xmpDM:startTime="2816900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="xi before plotting." xmpDM:startTime="2816900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="2816900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile plots y(i) is the observed qith quantile xi = theoretical qith quantile (xi, y(i)) plot should be a straight" xmpDM:startTime="2819900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="line To determine the qith quantile xi, need to invert the cumulative distribution function." xmpDM:startTime="2819900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="or Table 28.1" xmpDM:startTime="2819900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="lists the inverse of CDF for a number of distributions." xmpDM:startTime="2819900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp" xmpDM:startTime="2819900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile plots (Cont) Approximation for normal distribution N(0,1) For N(m, s), the xi values computed above are scaled to m+s" xmpDM:startTime="2824000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="xi before plotting." xmpDM:startTime="2824000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="2824000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plots: Example The difference between the values measured on a system and those predicted by a model is called" xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="modeling error." xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The modeling error for eight predictions of a model were found to be -0.04," xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.19," xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.14," xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.09," xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.14," xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.19," xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.04," xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 0.09." xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="2876733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plot: Example (Cont) chp_12_05" xmpDM:startTime="2944333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interpretation of Quantile-Quantile Data chp_12_06" xmpDM:startTime="2944433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plot: Example (Cont) chp_12_05" xmpDM:startTime="2945500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plots: Example The difference between the values measured on a system and those predicted by a model is called" xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="modeling error." xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The modeling error for eight predictions of a model were found to be -0.04," xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.19," xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.14," xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.09," xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.14," xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.19," xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.04," xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 0.09." xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="2964367" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plot: Example (Cont) chp_12_05" xmpDM:startTime="3020833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plots: Example The difference between the values measured on a system and those predicted by a model is called" xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="modeling error." xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The modeling error for eight predictions of a model were found to be -0.04," xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.19," xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.14," xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.09," xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.14," xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.19," xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.04," xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 0.09." xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="3090100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plot: Example (Cont) chp_12_05" xmpDM:startTime="3104867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interpretation of Quantile-Quantile Data chp_12_06" 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Data chp_12_06" xmpDM:startTime="3157000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary Sum of a large number of random variates is normally distributed." xmpDM:startTime="3273867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Central Tendencies: Mean, Median, Mode, Arithmetic, Geometric, Harmonic means Indices of Dispersion: Range, Variance, percentiles, Quartiles, SIQR Determining" xmpDM:startTime="3273867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Distribution of Data: Quantile-Quantile plots" xmpDM:startTime="3273867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interpretation of Quantile-Quantile Data chp_12_06" xmpDM:startTime="3295167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plot: Example (Cont) chp_12_05" xmpDM:startTime="3295967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interpretation of Quantile-Quantile Data chp_12_06" xmpDM:startTime="3383233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary Sum of a large number of random variates is normally distributed." xmpDM:startTime="3383567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Central Tendencies: Mean, Median, Mode, Arithmetic, Geometric, Harmonic means Indices of Dispersion: Range, Variance, percentiles, Quartiles, SIQR Determining" xmpDM:startTime="3383567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Distribution of Data: Quantile-Quantile plots" xmpDM:startTime="3383567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interpretation of Quantile-Quantile Data chp_12_06" xmpDM:startTime="3387867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plot: Example (Cont) chp_12_05" xmpDM:startTime="3388167" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description 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xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.04," xmpDM:startTime="3388633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 0.09." xmpDM:startTime="3388633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="3388633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plot: Example (Cont) chp_12_05" xmpDM:startTime="3389500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interpretation of Quantile-Quantile Data chp_12_06" xmpDM:startTime="3392600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plot: Example (Cont) chp_12_05" xmpDM:startTime="3400100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plots: Example The difference between the values measured on a system and those predicted by a model is called" xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="modeling error." xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The modeling error for eight predictions of a model were found to be -0.04," xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.19," xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.14," xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.09," xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.14," xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.19," xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.04," xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 0.09." xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="3400533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile plots (Cont) Approximation for normal distribution N(0,1) For N(m, s), the xi values computed above are scaled to m+s" xmpDM:startTime="3400833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="xi before plotting." xmpDM:startTime="3400833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="3400833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plots: Example The difference between the values measured on a system and those predicted by a model is called" xmpDM:startTime="3403600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="modeling error." xmpDM:startTime="3403600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The modeling 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Note: This data is" xmpDM:startTime="3595200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="available at the course website Please show the computation details (e.g.," xmpDM:startTime="3595200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Excel worksheet) used." xmpDM:startTime="3595200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Hint: Use Rank function in Excel." xmpDM:startTime="3595200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Remember to answer the 2nd question above." xmpDM:startTime="3595200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="3595200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary Sum of a large number of random variates is normally distributed." xmpDM:startTime="3669267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Central Tendencies: Mean, Median, Mode, Arithmetic, Geometric, Harmonic means Indices of Dispersion: Range, Variance, percentiles, Quartiles, SIQR Determining" xmpDM:startTime="3669267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Distribution of Data: Quantile-Quantile plots" xmpDM:startTime="3669267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interpretation of Quantile-Quantile Data chp_12_06" xmpDM:startTime="3670000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plot: Example (Cont) chp_12_05" xmpDM:startTime="3670433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plots: Example The difference between the values measured on a system and those predicted by a model is called" xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="modeling error." xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The modeling error for eight predictions of a model were found to be -0.04," xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.19," xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.14," xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.09," xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="-0.14," xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.19," xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.04," xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and 0.09." xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="3670900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantile-Quantile Plot: Example (Cont) chp_12_05" xmpDM:startTime="3686033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interpretation of Quantile-Quantile Data chp_12_06" xmpDM:startTime="3695200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summary Sum of a large number of random variates is normally distributed." xmpDM:startTime="3695600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Central Tendencies: Mean, Median, Mode, Arithmetic, Geometric, Harmonic means Indices of Dispersion: Range, Variance, percentiles, Quartiles, SIQR Determining" xmpDM:startTime="3695600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Distribution of Data: Quantile-Quantile plots" xmpDM:startTime="3695600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Homework 12B: Exercise 12.15" xmpDM:startTime="3696233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Plot a normal quantile-quantile plot for the following sample of errors: Are the errors normally distributed? 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