Effects of changes on mean and standard deviation

Informally, mean measures the location of the “center” while standard deviation measures the average distance from the mean.

This is more formally discussed in linear transformations of random variables (HL).

These may show up in 1- or 2-mark reasoning problems. When in doubt, just consider the effects to the sum (which is proportional to the mean), and average distance from the mean.

Systematic addition

Adding (or subtracting) all data by the same amount also adds (or subtract) the same amount to the mean.

Systematic addition or subtraction does not affect the standard deviation

Systematic multiplication

Multiplying all data by the same factor also multiplies both the mean and the standard deviation by the same factor.

more examples

Values above the mean are doubled; values below are halved.

Both mean and standard deviation increase.

Every second value is removed.

Both stay about the same, but it does depends on the data distribution.

Replacing few top values with few bottom values.

Mean decreases; standard deviation stays about the same.