How does dividing a value from each number in a set impact the standard deviation?

The standard deviation measures the amount of variation or dispersion in a set of values. When you divide every number in a set by a constant value, the effect on the standard deviation is significant. Specifically, the standard deviation becomes scaled by the same constant.

When you divide each value in the set by a number, the distances of each value from the mean are also divided by that same number. As a result, the overall spread of the data set changes in proportion to the constant you used for division. If the constant is greater than 1, the standard deviation decreases, and if the constant is less than 1 (but greater than 0), it increases. Therefore, the correct interpretation is that the standard deviation changes proportionally to the value by which the numbers were divided.

This understanding highlights the fundamental relationship between data scaling and standard deviation, showcasing the sensitivity of standard deviation to transformations of the data set.