Variance and Standard Deviation

What do the terms variance and standard deviation mean? How are these concepts related?

Both variance and standard deviation measure variability. Our textbook defines the variance as a measure of how spread out a set of scores is from the mean (Aron, Aron & Coups, 2009). It is the average of the squared deviations from the mean. The standard variation is the positive square root of the variance. The standard variation is a descriptive statistic whereas the variance is rarely used as descriptive. Standard variation is the most common descriptive statistic.

For example, while conducting research your numerical results are: 20, 14, 8, 5, and 3. First, you need to find the mean of these results. The mean is simply the average of these numbers.

(20+14+8+5+3)/5 = 50/5 = 10

The mean is 10. Next, subtract the mean from each number and square the result for each.

{[(20-10)²] + [(14-4)²] + [(8-10)²] + [(5-10)²] + [(3-10)²]}/ 5 = [100+16+4+25+49]/5

                                                                     = 194/5

                                                                  =38.8

The variance is 38.8.

Since the standard deviation is the square root of the variance.

√38.8 = 6.22

If rounded to the closest whole number, the standard deviation would be 6.

Aron, A., Aron, E. N., & Coups, E. J. (2009). Statistics for psychology (5th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.

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