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Unformatted text preview: In this lecture, we will discuss how to describe the variation in the data. Consider two samples of size 30, 40, 50, 60, 70, 80, 90 gG = 70 57, 58, 59, 60, 61, 62, 63 gG = 70 Both the sample data have the same mean . However, the values in the second data set are closer to the mean than the first data set. Some of the values in the first data set are far away from the mean they have a large ``spread as compared to the second data set. The first measure of variation is: Range = (maximum data value) (minimum data value) It is the difference between the maximum data value and the minimum data value. 30, 40, 50, 60, 70, 80, 90 gG = 70 range = (90 30) = 60 57, 58, 59, 60, 61, 62, 63 gG = 70 range = (63 57 ) = 6 It is very sensitive to extreme values; therefore not as useful as some other measures of variation. Another measure of variation: The standard deviation of a set of sample values, denoted by s (lower case) , is a measure of variation of values about the mean s = g G Shortcut: S = g G G Find the standard deviation s of the data {1, 3, 14}...
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This note was uploaded on 12/27/2011 for the course MATH 121 taught by Professor Banerjee during the Fall '11 term at Syracuse.
 Fall '11
 Banerjee
 Statistics, Probability

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