What effect does subtracting a value from each number in a set have on the standard deviation?

When a constant value is subtracted from each number in a set, the overall position of the numbers in the dataset is shifted, but the relative distances between the numbers remain unchanged. Standard deviation measures the amount of variation or dispersion in a set of values, essentially indicating how spread out the numbers are from the mean.

By subtracting a constant from each number, you are not altering how far the numbers are spread apart; you are simply moving the entire set up or down along the number line. Therefore, the standard deviation, which is influenced only by these distances, remains the same.

This principle is critical in understanding statistical measures, demonstrating that the standard deviation is invariant to shifts in the dataset. Such transformations affect the mean, but not the standard deviation, highlighting fundamental characteristics of how data behaves in statistical analyses.