The sample variance and sample standard deviation : s 2 s The sample variance s 2 and the sample standard deviation s provide an important measures of variation or spread in a set of data. The sample variance, loosely speaking, is the “average” squared distance from a data value (say y i ) to the sample average ¯ y of all data values; that is, the sample variance s 2 = ∑ n i =1 ( y i-¯ y ) 2 n-1 is an average of the squared deviation across all values y 1 ,y 2 ,...,y n in the data set. (Recall ¯ y again may be used as a measure of the central or typical value of the data, so with ( y i-¯ y ) 2 we access how spread the value y i is away from the center of the data ¯ y ). The more distant data values are from the sample mean ¯ y of the data, the larger the sample variance s 2 and the large the sample standard deviation s = √ s 2 . You should have learned how to compute the standard deviation of a set of numbers in your introductory statistics class. In case you have forgotten or never learned, the example below shows how to compute the standard deviation of a small data set. Usually we use a computer to ﬁnd standard deviations, but you should
This is the end of the preview.
access the rest of the document.