The relationship of the standard deviation to the normal curve makes it possible to compare groups of scores if they come from distributions that are approximately normal.

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The standard deviation is a measure of the spread of scores in a distribution, and when the distribution is approximately normal, it follows a specific pattern that can be represented by the normal curve. Therefore, when comparing groups of scores that come from distributions that are approximately normal, the standard deviation can be used to assess how much variation there is within each group and to compare the groups based on their relative dispersion.

The Relationship of the Standard Deviation to the Normal Curve