Section3-3

Section3-3 - Measures of Variation A Bourhim Syracuse...

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Measures of Variation A. Bourhim Syracuse University MAT121-Fall 2011 A. Bourhim (Syracuse University) Measures of Variation MAT121-Fall 2011 1 / 12
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Introduction It is important to know whether the data values are very spread out and whether they clump together near the center. The variance is used as a measure of how far a set of numbers are spread out from each other, and also describes how far the data values lie from the mean. In this section, we learn about range, standard deviation, variance and coefficient of variation. Range Range = maximum value - minimum value . Remark The range is very easy to compute but not very useful. Example The range of 1 , 4 , 17 , 6 , 41 , 30 is range = 41 - 1 = 40 . A. Bourhim (Syracuse University) Measures of Variation MAT121-Fall 2011 2 / 12
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Standard deviation Sample Standard Deviation Formula The standard deviation of a sample is s = s ( x - x ) 2 n - 1 . Or the shortcut formula s = v u u u u t n ( x 2 ) - ± x 2 n ( n - 1 ) . The variance of a sample is s 2 , the square of the standard deviation. 2 A. Bourhim (Syracuse University) Measures of Variation MAT121-Fall 2011 3 / 12
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Example Consider the following sample 1 , 4 , 5 , 2 , 4 , and find s and s 2 . To use the first formula: 1 Find n and x . We have n = 5 and x = 1 + 4 + 5 + 2 + 4 5 = 3 . 2 . 2 For each data value x , find the difference x - x and then square it.
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This note was uploaded on 10/06/2011 for the course MAT 121 taught by Professor Quinn during the Fall '08 term at Syracuse.

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Section3-3 - Measures of Variation A Bourhim Syracuse...

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