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                           <rdf:li><rdf:Description xmpDM:name="Mean, Variance, CoV Mean or Expected Value: Variance: The expected value of the square of distance between x and its" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="mean Coefficient of Variation: TP_tmp TP_tmp TP_tmp" xmpDM:startTime="0" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean, Variance, CoV: Examples Mean or Expected Value: Variance: Standard Deviation: Coefficient of Variation: TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="143267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Covariance and Correlation Covariance: For independent variables, the covariance is zero: Although independence always implies zero covariance, the reverse is" xmpDM:startTime="151433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="not true." xmpDM:startTime="151433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Correlation Coefficient: normalized value of covariance The correlation always lies between -1 and +1." xmpDM:startTime="151433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp TP_tmp" xmpDM:startTime="151433" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean and Variance of Sums If are k random variables and if are k arbitrary constants (called weights), then: For" xmpDM:startTime="208800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="independent variables: TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="208800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantiles, Median, and Mode Quantile: The x value at which the CDF takes a value a is called the a-quantile" xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="or 100a-percentile." xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It is denoted by xa: Median: The 50-percentile or (0.5-quantile)" xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="of a random variable is called its median." xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mode: The most likely value, that is, xi that has the highest probability pi, or the x at which pdf" xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is maximum, is called mode of x." xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp 1.00" xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.00" xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="x F(x) 0.25" xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.50" xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.75" xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="f(x) x" xmpDM:startTime="228567" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Normal Distribution Normal Distribution: The sum of a large number of independent observations from any distribution with a finite variance" xmpDM:startTime="314733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="has a normal distribution." xmpDM:startTime="314733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="A normal variate is denoted at N(m,s)." xmpDM:startTime="314733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Unit Normal: A normal distribution with zero mean and unit variance." xmpDM:startTime="314733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Also called standard normal distribution and is denoted as N(0,1)." xmpDM:startTime="314733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="314733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Normal Quantiles An a-quantile of a unit normal variate z» N(0,1) is denoted by za." xmpDM:startTime="444600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="If a random variable x has a N(m, s) distribution, then (x-m)/s has a N(0,1) distribution." xmpDM:startTime="444600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="or TP_tmp TP_tmp" xmpDM:startTime="444600" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Normal Distribution Normal Distribution: The sum of a large number of independent observations from any distribution with a finite variance" xmpDM:startTime="448800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="has a normal distribution." xmpDM:startTime="448800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="A normal variate is denoted at N(m,s)." xmpDM:startTime="448800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Unit Normal: A normal distribution with zero mean and unit variance." xmpDM:startTime="448800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Also called standard normal distribution and is denoted as N(0,1)." xmpDM:startTime="448800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="448800" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Quantiles, Median, and Mode Quantile: The x value at which the CDF takes a value a is called the a-quantile" xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="or 100a-percentile." xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It is denoted by xa: Median: The 50-percentile or (0.5-quantile)" xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="of a random variable is called its median." xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mode: The most likely value, that is, xi that has the highest probability pi, or the x at which pdf" xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="is maximum, is called mode of x." xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp 1.00" xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.00" xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="x F(x) 0.25" xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.50" xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="0.75" xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="f(x) x" xmpDM:startTime="449267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Normal Distribution Normal Distribution: The sum of a large number of independent observations from any distribution with a finite variance" xmpDM:startTime="572700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="has a normal distribution." xmpDM:startTime="572700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="A normal variate is denoted at N(m,s)." xmpDM:startTime="572700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Unit Normal: A normal distribution with zero mean and unit variance." xmpDM:startTime="572700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Also called standard normal distribution and is denoted as N(0,1)." xmpDM:startTime="572700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="572700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Normal Quantiles An a-quantile of a unit normal variate z» N(0,1) is denoted by za." xmpDM:startTime="572933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="If a random variable x has a N(m, s) distribution, then (x-m)/s has a N(0,1) distribution." xmpDM:startTime="572933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="or TP_tmp TP_tmp" xmpDM:startTime="572933" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Why Normal? There are two main reasons for the popularity of the normal distribution: The sum of n independent normal" xmpDM:startTime="587467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="variates is a normal variate." xmpDM:startTime="587467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="If, then x=åi=1n ai xi has a normal distribution with mean m=åi=1n ai mi and variance s2=åi=1n ai2si2." xmpDM:startTime="587467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The sum of a large number of independent observations from any distribution tends to have a normal distribution." xmpDM:startTime="587467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="This result, which is called central limit theorem, is true for observations from all distributions with finite variances Þ Experimental" xmpDM:startTime="587467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="errors caused by many factors are normal." xmpDM:startTime="587467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="587467" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Homework 12A: Exercise 12.7" xmpDM:startTime="689833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="The execution times of queries on a database is normally distributed with a mean of 5 seconds and a standard" xmpDM:startTime="689833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="deviation of 1 second." xmpDM:startTime="689833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Determine the following: What is the probability of the execution time being more than 8 seconds." xmpDM:startTime="689833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="What is the probability of the execution time being less than 6 seconds." xmpDM:startTime="689833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="What percent of responses will take between 4 and 7 seconds? What is the 95-percentile execution time? (Remember to use" xmpDM:startTime="689833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the correct table) Show details not just the final result." xmpDM:startTime="689833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="689833" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summarizing Data by a Single Number Indices of central tendencies: Mean, Median, Mode Sample Mean is obtained by taking the" xmpDM:startTime="1356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="sum of all observations and dividing this sum by the number of observations in the sample." xmpDM:startTime="1356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Sample Median is obtained by sorting the observations in an increasing order and taking the observation that is in the" xmpDM:startTime="1356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="middle of the series." xmpDM:startTime="1356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="If the number of observations is even, the mean of the middle two values is used as a median." xmpDM:startTime="1356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Sample Mode is obtained by plotting a histogram and specifying the midpoint of the bucket where the histogram peaks." xmpDM:startTime="1356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For categorical variables, mode is given by the category that occurs most frequently." xmpDM:startTime="1356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean and median always exist and are unique." xmpDM:startTime="1356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mode, on the other hand, may not exist." xmpDM:startTime="1356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="1356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean, Median, and Mode: Relationships chp_12_01" xmpDM:startTime="1591033" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting Mean, Median, and Mode chp_12_02" xmpDM:startTime="1920000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean, Median, and Mode: Relationships chp_12_01" xmpDM:startTime="2062000" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting Mean, Median, and Mode chp_12_02" xmpDM:startTime="2092700" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Central Tendencies: Examples Most used resource in a system: Resources are categorical and hence mode must be used." xmpDM:startTime="2169233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interarrival time: Total time is of interest and so mean is the proper choice." xmpDM:startTime="2169233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Load on a Computer: Median is preferable due to a highly skewed distribution." xmpDM:startTime="2169233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Average Configuration: Medians of number devices, memory sizes, number of processors are generally used to specify the configuration due to" xmpDM:startTime="2169233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the skewness of the distribution." xmpDM:startTime="2169233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2169233" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting Mean, Median, and Mode chp_12_02" xmpDM:startTime="2339067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Central Tendencies: Examples Most used resource in a system: Resources are categorical and hence mode must be used." xmpDM:startTime="2412733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interarrival time: Total time is of interest and so mean is the proper choice." xmpDM:startTime="2412733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Load on a Computer: Median is preferable due to a highly skewed distribution." xmpDM:startTime="2412733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Average Configuration: Medians of number devices, memory sizes, number of processors are generally used to specify the configuration due to" xmpDM:startTime="2412733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the skewness of the distribution." xmpDM:startTime="2412733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2412733" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Selecting Mean, Median, and Mode chp_12_02" xmpDM:startTime="2458067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Central Tendencies: Examples Most used resource in a system: Resources are categorical and hence mode must be used." xmpDM:startTime="2465100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Interarrival time: Total time is of interest and so mean is the proper choice." xmpDM:startTime="2465100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Load on a Computer: Median is preferable due to a highly skewed distribution." xmpDM:startTime="2465100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Average Configuration: Medians of number devices, memory sizes, number of processors are generally used to specify the configuration due to" xmpDM:startTime="2465100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="the skewness of the distribution." xmpDM:startTime="2465100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="2465100" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Common Misuses of Means Using mean of significantly different values: (10+1000)/2 = 505 Using mean without regard to the skewness" xmpDM:startTime="2465633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="of distribution." xmpDM:startTime="2465633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="2465633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Misuses of Means (cont) Multiplying means to get the mean of a product Example: On a timesharing system, Average number" xmpDM:startTime="2925967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="of users is 23 Average number of sub-processes per user is 2 What is the average number of sub-processes? Is" xmpDM:startTime="2925967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="it 46? No! The number of sub-processes a user spawns depends upon how much load there is on the system." xmpDM:startTime="2925967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Taking a mean of a ratio with different bases." xmpDM:startTime="2925967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Already discussed in Chapter 11 on ratio games and is discussed further later TP_tmp" xmpDM:startTime="2925967" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Geometric Mean Geometric mean is used if the product of the observations is a quantity of interest." xmpDM:startTime="3047333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="3047333" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Geometric Mean: Example The performance improvements in 7 layers: TP_tmp TP_tmp" xmpDM:startTime="3185867" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Examples of Multiplicative Metrics Cache hit ratios over several levels of caches Cache miss ratios Percentage performance improvement between successive" xmpDM:startTime="3356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="versions Average error rate per hop on a multi-hop path in a network." xmpDM:startTime="3356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="" xmpDM:startTime="3356633" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Geometric Mean of Ratios The geometric mean of a ratio is the ratio of the geometric means of the numerator" xmpDM:startTime="3482533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="and denominator Þ the choice of the base does not change the conclusion." xmpDM:startTime="3482533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="It is because of this property that sometimes geometric mean is recommended for ratios." xmpDM:startTime="3482533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="However, if the geometric mean of the numerator or denominator do not have any physical meaning, the geometric mean of" xmpDM:startTime="3482533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="their ratio is meaningless as well." xmpDM:startTime="3482533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="3482533" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Harmonic Mean Used whenever an arithmetic mean can be justified for 1/xi E.g.," xmpDM:startTime="3600400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Elapsed time of a benchmark on a processor In the ith repetition, the benchmark takes ti seconds." xmpDM:startTime="3600400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Now suppose the benchmark has m million instructions, MIPS xi computed from the ith repetition is: ti's should be summarized" xmpDM:startTime="3600400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="using arithmetic mean since the sum of t_i has a physical meaning Þ xi's should be summarized using harmonic mean" xmpDM:startTime="3600400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="since the sum of 1/xi's has a physical meaning." xmpDM:startTime="3600400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp TP_tmp" xmpDM:startTime="3600400" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Harmonic Mean (Cont) The average MIPS rate for the processor is: However, if xi's represent the MIPS rate for n" xmpDM:startTime="3772300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="different benchmarks so that ith benchmark has mi million instructions, then harmonic mean of n ratios mi/ti cannot be used" xmpDM:startTime="3772300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="since the sum of the ti/mi does not have any physical meaning." xmpDM:startTime="3772300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Instead, as shown later, the quantity å mi/å ti is a preferred average MIPS rate." xmpDM:startTime="3772300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="3772300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Weighted Harmonic Mean The weighted harmonic mean is defined as follows: where, wi's are weights which add up to one:" xmpDM:startTime="3852267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="All weights equal Þ Harmonic, I.e.," xmpDM:startTime="3852267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="wi=1/n." xmpDM:startTime="3852267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="In case of MIPS rate, if the weights are proportional to the size of the benchmark: Weighted harmonic mean would" xmpDM:startTime="3852267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="be: TP_tmp TP_tmp TP_tmp TP_tmp" xmpDM:startTime="3852267" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean of A Ratio If the sum of numerators and the sum of denominators, both have a physical meaning, the" xmpDM:startTime="3899900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="average of the ratio is the ratio of the averages." xmpDM:startTime="3899900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="For example, if xi=ai/bi, the average ratio is given by: TP_tmp" xmpDM:startTime="3899900" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean of a Ratio: Example CPU utilization TP_tmp" xmpDM:startTime="4139500" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example (Cont) Ratios cannot always be summarized by a geometric mean." xmpDM:startTime="4277767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="A geometric mean of utilizations is useless." xmpDM:startTime="4277767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="4277767" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean of a Ratio: Special Cases If the denominator is a constant and the sum of numerator has a physical" xmpDM:startTime="4298200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="meaning, the arithmetic mean of the ratios can be used." xmpDM:startTime="4298200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="That is, if bi=b for all i's, then: Example: mean resource utilization." xmpDM:startTime="4298200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="TP_tmp" xmpDM:startTime="4298200" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean of Ratio (Cont) If the sum of the denominators has a physical meaning and the numerators are constant then" xmpDM:startTime="4332300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="a harmonic mean of the ratio should be used to summarize them." xmpDM:startTime="4332300" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="That is, if ai=a for all i's, then: Example: MIPS using the same benchmark TP_tmp" xmpDM:startTime="4332300" 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="4355067" 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="4355067" xmpDM:duration="1000"/></rdf:li><rdf:li><rdf:Description xmpDM:name="of ai/bi." xmpDM:startTime="4355067" 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="4355067" 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="4355067" 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="4355067" xmpDM:duration="1000"/></rdf:li></rdf:Seq>
                     </xmpDM:markers>
                  </rdf:Description>
               </rdf:li>
               <rdf:li>
                  <rdf:Description xmpDM:trackType="TableOfContents" xmpDM:frameRate="f1000" xmpDM:trackName="Table of Contents">
                     <xmpDM:markers>
                        <rdf:Seq>
                           <rdf:li><rdf:Description xmpDM:name="Mean, Variance, CoV" xmpDM:startTime="0" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="0" tscDM:imageoffset="0" tscDM:imagerect="0, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="   Mean, Variance, CoV: Examples" xmpDM:startTime="143267" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="1" tscDM:imageoffset="0" tscDM:imagerect="75, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Covariance and Correlation" xmpDM:startTime="151433" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="2" tscDM:imageoffset="0" tscDM:imagerect="150, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean and Variance of Sums" xmpDM:startTime="208800" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="3" tscDM:imageoffset="0" tscDM:imagerect="225, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="         Quantiles, Median, and Mode" xmpDM:startTime="228567" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="4" tscDM:imageoffset="0" tscDM:imagerect="300, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Normal Distribution" xmpDM:startTime="314733" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="5" tscDM:imageoffset="0" tscDM:imagerect="375, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Normal Quantiles" xmpDM:startTime="444600" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="6" tscDM:imageoffset="0" tscDM:imagerect="450, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Normal Distribution" xmpDM:startTime="448800" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="7" tscDM:imageoffset="0" tscDM:imagerect="525, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="         Quantiles, Median, and Mode" xmpDM:startTime="449267" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="8" tscDM:imageoffset="0" tscDM:imagerect="600, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Normal Distribution" xmpDM:startTime="572700" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="9" tscDM:imageoffset="0" tscDM:imagerect="675, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name=" Normal Quantiles" xmpDM:startTime="572933" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="10" tscDM:imageoffset="0" tscDM:imagerect="750, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Why Normal?" xmpDM:startTime="587467" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="11" tscDM:imageoffset="0" tscDM:imagerect="825, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="       Homework 12A: Exercise 12.7 " xmpDM:startTime="689833" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="12" tscDM:imageoffset="0" tscDM:imagerect="900, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Summarizing Data by a Single Number" xmpDM:startTime="1356633" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="13" tscDM:imageoffset="0" tscDM:imagerect="975, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean, Median, and Mode: Relationships " xmpDM:startTime="1591033" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="14" tscDM:imageoffset="0" tscDM:imagerect="1050, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="  Selecting Mean, Median, and Mode" xmpDM:startTime="1920000" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="15" tscDM:imageoffset="0" tscDM:imagerect="1125, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean, Median, and Mode: Relationships " xmpDM:startTime="2062000" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="16" tscDM:imageoffset="0" tscDM:imagerect="1200, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="  Selecting Mean, Median, and Mode" xmpDM:startTime="2092700" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="17" tscDM:imageoffset="0" tscDM:imagerect="1275, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Central Tendencies: Examples" xmpDM:startTime="2169233" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="18" tscDM:imageoffset="0" tscDM:imagerect="1350, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="  Selecting Mean, Median, and Mode" xmpDM:startTime="2339067" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="19" tscDM:imageoffset="0" tscDM:imagerect="1425, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Central Tendencies: Examples" xmpDM:startTime="2412733" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="20" tscDM:imageoffset="0" tscDM:imagerect="1500, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="  Selecting Mean, Median, and Mode" xmpDM:startTime="2458067" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="21" tscDM:imageoffset="0" tscDM:imagerect="1575, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Indices of Central Tendencies: Examples" xmpDM:startTime="2465100" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="22" tscDM:imageoffset="0" tscDM:imagerect="1650, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Common Misuses of Means" xmpDM:startTime="2465633" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="23" tscDM:imageoffset="0" tscDM:imagerect="1725, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Misuses of Means (cont)" xmpDM:startTime="2925967" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="24" tscDM:imageoffset="0" tscDM:imagerect="1800, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Geometric Mean" xmpDM:startTime="3047333" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="25" tscDM:imageoffset="0" tscDM:imagerect="1875, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Geometric Mean: Example" xmpDM:startTime="3185867" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="26" tscDM:imageoffset="0" tscDM:imagerect="1950, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Examples of Multiplicative Metrics" xmpDM:startTime="3356633" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="27" tscDM:imageoffset="0" tscDM:imagerect="2025, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Geometric Mean of Ratios" xmpDM:startTime="3482533" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="28" tscDM:imageoffset="0" tscDM:imagerect="2100, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Harmonic Mean" xmpDM:startTime="3600400" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="29" tscDM:imageoffset="0" tscDM:imagerect="2175, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Harmonic Mean (Cont)" xmpDM:startTime="3772300" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="30" tscDM:imageoffset="0" tscDM:imagerect="2250, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Weighted Harmonic Mean" xmpDM:startTime="3852267" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="31" tscDM:imageoffset="0" tscDM:imagerect="2325, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean of A Ratio" xmpDM:startTime="3899900" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="32" tscDM:imageoffset="0" tscDM:imagerect="2400, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean of a Ratio: Example" xmpDM:startTime="4139500" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="33" tscDM:imageoffset="0" tscDM:imagerect="2475, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Example (Cont)" xmpDM:startTime="4277767" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="34" tscDM:imageoffset="0" tscDM:imagerect="2550, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="      Mean of a Ratio: Special Cases" xmpDM:startTime="4298200" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="35" tscDM:imageoffset="0" tscDM:imagerect="2625, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean of Ratio (Cont)" xmpDM:startTime="4332300" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="36" tscDM:imageoffset="0" tscDM:imagerect="2700, 0, 75, 56"/></rdf:li><rdf:li><rdf:Description xmpDM:name="Mean of Ratios (Cont)" xmpDM:startTime="4355067" tscDM:image="k_12smd2_Thumbnails.png" tscDM:imageindex="37" tscDM:imageoffset="0" tscDM:imagerect="2775, 0, 75, 56"/></rdf:li></rdf:Seq>
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         </xmpDM:Tracks>
         <tscDM:controller>
            <rdf:Description xmpDM:name="tscplayer">
               <tscDM:parameters>
                  <rdf:Bag>
                     <rdf:li xmpDM:name="autohide" xmpDM:value="true"/><rdf:li xmpDM:name="autoplay" xmpDM:value="false"/><rdf:li xmpDM:name="loop" xmpDM:value="false"/><rdf:li xmpDM:name="searchable" xmpDM:value="true"/><rdf:li xmpDM:name="captionsenabled" xmpDM:value="false"/><rdf:li xmpDM:name="sidebarenabled" xmpDM:value="false"/><rdf:li xmpDM:name="unicodeenabled" xmpDM:value="false"/><rdf:li xmpDM:name="backgroundcolor" xmpDM:value="000000"/><rdf:li xmpDM:name="sidebarlocation" xmpDM:value="left"/><rdf:li xmpDM:name="endaction" xmpDM:value="stop"/><rdf:li xmpDM:name="endactionparam" xmpDM:value="true"/><rdf:li xmpDM:name="locale" xmpDM:value="en-US"/></rdf:Bag>
               </tscDM:parameters>
               <tscDM:controllerText>
                  <rdf:Bag>
                  </rdf:Bag>
               </tscDM:controllerText>
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         </tscDM:controller>
         <tscDM:contentList>
            <rdf:Description>
               <tscDM:files>
                  <rdf:Seq>
                     <rdf:li xmpDM:name="0" xmpDM:value="k_12smd2.mp4"/><rdf:li xmpDM:name="1" xmpDM:value="k_12smd2_First_Frame.png"/><rdf:li xmpDM:name="2" xmpDM:value="k_12smd2_Thumbnails.png"/></rdf:Seq>
               </tscDM:files>
            </rdf:Description>
         </tscDM:contentList>
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</x:xmpmeta>