Chapter 2.4, Problem 51E

Alternative Formula You used $S{S}_x=\Sigma {(x-\bar{x})}^2$ when calculating variance and standard deviation. An alternative formula that is sometimes more convenient for hand calculations is

$S{S}_x=\Sigma x^2-\frac{{(\Sigma x)}^2}{n}.$

You can find the sample variance by dividing the sum of squares by n − 1 and the sample standard deviation by finding the square root of the sample variance.

1. (a) Show how to obtain the alternative formula.
2. (b) Use the alternative formula to calculate the sample standard deviation for the data set in Exercise 15.
3. (c) Compare your result with the sample standard deviation obtained in Exercise 15.