Variance and Standard Deviation
(A worked Problem:  Procedure explained in more detail in Chapter 5)

A clinical psychologist has recorded the numbers of compulsive acts performed each day during the last week by a person with obsessive-compulsive disorder.
Compute the mean, variance and standard deviaiton of these scores:

23, 34, 24, 18, 23, 26, 20

I. Compute the Mean

A. Sum the scores

B. Divide the sum of the scores by n (remember n is the number of scores, 7)

II. Comput the variance

A. Deviation Method

1. Subtract the mean from each score to create mean deviations

2. Square each mean deviation and sum the squared deviations

3. The variance is the sum of the squared deviations divided by n-1

B. The computational formula

1. Square each X

2. Use the computational formula to compute the variance

Hint:    Remember to square each X to get the sum of the X squared.
           Remember to square the sum of the X's to get the sum of the X the quantity squared

II. The Standard Deviation is the square root of the Variance

or

Hint:    Remember just push the square root key after you compute the variance.

III.  Visual Summary:  Computational Formulas for the Variance and the Standard Deviation

Copyright © 2004 by Mark W. Vernoy