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Chris Morgan, MATH G160 csmorgan@purdue.edu April 18, 2012 Lecture 31

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##### Chris Morgan, MATH G160 csmorgan@purdue.edu April 18, 2012 Lecture 31

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**Chris Morgan, MATH G160**csmorgan@purdue.edu April 18, 2012 Lecture 31 Chapter 3.2 & 3.5: Variance, Covariance, and Correlation**Two different machines produce products with weights as**follows: • Machine 1: 99 97 98 101 101 101 102 100 100 101 • Machine 2: 90 105 110 85 110 95 102 103 110 90 • mean of machine 1 = mean of machine 2 = 100 • Even though means are equivalent, very different outputs • Variance is the measure of difference between the value of each observation and the mean. Why do we care about Variability?**Example (I)**Age of 40 students in the room today: 20 21 20 22 20 23 21 22 23 24 21 19 20 22 21 22 18 19 19 … Population (all 40 students): mean = 22.32 variance: 18 Sample of size 5: 20 21 20 23 21 mean = 21 variance: 1.5 Standard Deviation is the square root of variance and is denoted by sigma, σ. Population standard deviation: sqrt(18) = 4.24 Sample standard deviation: sqrt(1.5) = 1.22**Example (II)**Number of wins by Minnesota Vikings last 10 seasons: 9 7 8 12 10 9 5 7 8 9 Population (all 10 seasons): mean = 8.4 variance: 40.2/10 = 4.02 Sample of size 4: 9 12 5 7 mean = 8.25 variance: 26.75/3 = 8.92**Coefficient of Variation**• Coefficient of variation is the ratio of standard deviation to mean • Takes both location and variability into consideration • Reflect the relative variability of a population of sample**Covariance and Correlation Coefficient**• • Measure the linear association between two variables, X and Y • • X is not necessarily a dependent variable • • The population size or sample size of X and Y must equal • Correlation Coefficient represented by r**Example (III)**• X: = 8.375, s2X = 17.98, sx = 4.24 • Y: = 18.31, s2Y =193.43, sy = 13.91 • sXY = 52.54 • r = sxy/(sx*sy) = 52.54 / (4.24*13.91) = 0.89**Example (IV)**You give out a satisfaction survey to your employees (Executives and Middle Managers) and they rate their satisfaction on a scale of 1 to 5, 1 being least satisfied and 5 being most satisfied. You find the following: Executives: Mean score = 4.0 Standard Deviation = 1.7 Middle Managers: Mean score = 3.5 Standard Deviation = .8 • What does this tell you about your employees? • Using this data, what would you want to do to try to improve your employee satisfaction? How would it be different for Middle Managers and Executives? Why?**Example (V)**In this company that you’re running, you decide to have a supplier ship office supplies every month to keep your inventory up and your employees happy. You look into a couple different suppliers of their time to ship: • Which supplier would you go with and why? • What other factors would you want to see before you make your decision?