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Chapter 3 sec 2

# Chapter 3 sec 2 - MeasuresofVariation Chapter3 Section2...

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Measures of Variation Chapter 3  Section 2 1 Mr. Kenneth Horwitz October 13, 2010

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Measures of Variation How Can We Measure Variability? Range Variance Standard Deviation Coefficient of Variation Chebyshev’s Theorem Empirical Rule (Normal) 2
Measures of Variation: Range The  range  is the difference between the highest and  lowest values in a data set.   3 R Highest Lowest = -

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Outdoor Paint Two experimental brands of outdoor paint are tested  to see how long each will last before fading.  Six cans  of each brand constitute a small population. The  results (in months) are shown. Find the mean and  range of each group. 4 Brand A Brand B 10 35 60 45 50 30 30 35 40 40 20 25
Outdoor Paint 5 Brand A Brand B 10 35 60 45 50 30 30 35 40 40 20 25 The average for both brands is the same, but the range for Brand A is much greater than the range for Brand B. Which brand would you buy? 210 35 Brand A: 6 60 10 50 X N R μ = = = - = = 210 35 Brand B: 6 45 25 20 X R N μ = = = - = =

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Measures of Variation: Variance  & Standard Deviation The  variance  is the average of the squares of the  distance each value is from the mean.   The  standard deviation  is the square root of the  variance. The standard deviation is a measure of how  spread out your data are. 6
Uses of the Variance and  Standard Deviation To determine the spread of the data. To determine the consistency of a variable. To determine the number of data values that fall  within a specified interval in a distribution  (Chebyshev’s Theorem).

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