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The standard deviation quantifies the average distance of scores from the mean. For example, when comparing two distributions with the same mean of $$10$$, a distribution where scores are tightly clustered near the center might have a standard deviation of $$1.69$$, meaning scores differ from the mean by about $$1.69$$ units on average. In contrast, a distribution with scores spread across a broader range might have a standard deviation of $$4.30$$, meaning scores differ from the mean by about $$4.30$$ units on average.

Example of Standard Deviations in Distributions

If two distributions of scores have the same mean, the distribution in which scores are more tightly clustered around the mean will have a larger standard deviation than the distribution in which scores are more spread out.

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