A more informative measure of variability is the variance, which represents the variability of scores around their group mean. Unlike the range, the variance takes into account every score in the distribution. As mentioned previously, the measure of variability tells us how well the measure of central tendency portrays the entire set of data. Recall the example in Table 2 focusing on the book sales of two representatives? Both representatives sold an average of 12.5 books per month, but the value 12.5 was a better representation of Mr. Smith’s sales than of Ms. Johnson’s. Why? Because if we were asked to predict how many books these representatives would sell next month, a guess of 12.5 would probably be very close to Mr. Smith’s sales but not very close to Ms. Johnson’s actual sales. The variance is a numerical way of describing the degree to which the scores in a data set differ or fluctuate from the mean value. Technically, the variance is the average of the squared deviations from the mean.

Suppose you wanted to calculate the variances for the representatives’ book sales data. First, find the mean for each representative. We already know this to be 12.5 for each. Second, find the deviation of each score from the appropriate representative’s mean. Note that deviation scores will be negative for scores that are below the mean. As a check on your calculations, the sum of the deviation scores should equal zero. Third, square the deviation scores. By squaring the scores, negative scores are made positive and extreme scores are given relatively more weight. Fourth, find the sum of the squared deviation scores. This sum has a special name, sum of squares, and it is used in many statistical calculations. Fifth, divide the sum by the number of scores. This yields the variance. Calculation of the variance for Mr. Smith’s data is shown in Table 3. The variance is .917.

Table 3.

X	X - M	(X – M)2
12	12 – 12.5 = -.5	.25
13	13 – 12.5 = .5	.25
12	12 – 12.5 = -.5	.25
14	14 – 12.5 = 1.5	2.25
11	11 – 12.5 = -1.5	2.25
13	13 – 12.5 = .5	.25
		SUM = 5.5

Variance = 5.5/6 = .917. Now calculate the variance for Ms. Johnson’s sales. Her variance is 51.583!