When a value is subtracted from each number in a set, what happens to the variance?

When a constant value is subtracted from each number in a set, the variance of the set remains unchanged. Variance measures the degree to which numbers in a dataset are spread out from their mean.

The calculation of variance involves the average of the squared differences from the mean. When you subtract a constant from each number, it shifts the entire set of data points uniformly without affecting the differences between them. As a result, while the mean of the dataset will change, the distances between each data point and the mean remain the same. Consequently, the squared differences, and therefore the variance, do not change.

It’s important to recognize that variance is not dependent on the actual numbers in the dataset but rather on how those numbers relate to one another. Since the subtraction does not affect these relationships among the numbers, the variance remains unchanged.