If you were to add 5 to each value in a data set, what effect would this have on the standard deviation of the data set?
Adding 5 to every value in a data set has no effect on the standard deviation of the data set.
Recall that the formula for standard deviation of a sample is:
Of the terms in the equation,
Thus, when calculating our standard deviation for the new
As a general rule, the median, mean, and quartiles will be changed by adding a constant to each value. However, the range, interquartile range, standard deviation and variance will remain the same. Multiplying every value by a constant, however, will multiply the mean, median, quartiles, range, interquartile range, and standard deviation by that constant, and multiply the variance (which is simply the square of the standard deviation) by the square of that constant.
Adding a constant to each value in a data set does not change the distance between values so the standard deviation remains the same.
For example, consider the following numbers
If we were to add 5 to each value in this data set, the new set of values would be:
As you can see the s.d. remains the same unless you multiply every value by a constant.