What Is the Standard Deviation, and How Is It Computed?

What Is the Standard Deviation, and How Is It Computed?

The standard deviation (represented by a lowercase s) is a measure of how much, on average, each score in a set of scores varies from the average (usually the mean) of that set of scores. One of several measures of variability, it is used to assess how much variability or diversity there is in any one set of scores.

It is computed by finding the average amount that each score deviates from the average of all the scores in the data set.

The formula is

$$s=\sqrt{\frac{\sum {\left(X-\overline{X}\right)}^2}{n-1}}$$

Here’s an example using a very simple set of scores, which represent the number of correct words on a 20-item spelling test.

• 16
• 14
• 10
• 15
• 14
• 12
• 19
• 15
• 8
• 7

[Page 42]And, here are the steps for computing the standard deviation:

• 1.
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