Which measure would not change if a constant is added to every data value?

The standard deviation is a measure of the amount of variation or dispersion in a set of data values. When a constant is added to every value in a data set, the spread or dispersion of the values does not change; only their location along the number line shifts.

For instance, if you have a set of data values (like test scores) and you add a constant (like 5 points) to each score, the relative distances between the scores remain the same. This is because standard deviation calculates how much each data point deviates from the mean, and if you add a constant to each score, the mean will also increase by that same constant. Therefore, the differences between each score and the mean remain unchanged.

In contrast, measures like range, variance, and sum would all change with the addition of a constant. The range would be affected as both the maximum and minimum values increase, thus altering the difference between them. Variance would change as it is based on the deviations of each score from the mean, which now reflects new values. Lastly, the sum of the data values will obviously increase by the total number of data points multiplied by the constant added.