Multiple choice

The standard deviation of a data set is 6. If each observation is multiplied by 3 and then 5 is subtracted from the result, what will be the new standard deviation?

  1. 6

  2. 13

  3. 18

  4. 23

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Standard deviation is invariant under translation (subtracting 5) but scales with multiplication. New SD = |3| * Old SD = 3 * 6 = 18.

AI explanation

When each observation of a data set is multiplied by a constant, the standard deviation is also multiplied by that same constant. Adding or subtracting a constant from every observation does not change the standard deviation, as it only shifts the distribution. Multiplying the original standard deviation of 6 by 3 gives a new standard deviation of 18.