Comparing standard deviations of two unknown lists

Question

Consider the following problem:

• List A contains 15 numbers in the range from 10 to 50.
• List B contains 15 numbers in the range from -50 to -10.

Or any other two lists.

Is there some trick to compare the standard deviations of the two lists without even knowing what the actual numbers are?

Answer 1

No, there isn't.

Counterexample:

• The list (10, 10, 10, ..., 10) has the standard deviation 0. The list (-50, -10, -50, -10, ..., -50) has a standard deviation of approximately 19.9555.

• The list (10, 50, 10, 50, ..., 10) has a standard deviation of approximately 19.9555. The list (-10, -10, -10, ..., -10) has the standard deviation 0.

More generally, note that adding a constant value to all elements of a list does not change the standard deviation of the list. Thus, as your intervals have the same length, for any list of numbers in the first interval, there is a list of numbers in the second interval with the same standard deviation, and vice versa.