Multiple choice

The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, what will be the new mean and the new standard deviation, respectively?

  1. 45, 5

  2. 11.25, 1.25

  3. 11.25, 2.5

  4. 12.5, 2.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If each observation x is transformed to (x-a)/b, the new mean is (mean-a)/b and the new standard deviation is SD/|b|. Here a=5, b=4. New mean = (50-5)/4 = 45/4 = 11.25. New SD = 10/4 = 2.5.

AI explanation

When a constant value is subtracted from a set of observations, the mean decreases by that constant, but the standard deviation remains unchanged; therefore, subtracting 5 makes the new mean 45. When the observations are divided by a constant, both the mean and the standard deviation are divided by that same constant. Dividing the mean of 45 by 4 gives 11.25, and dividing the standard deviation of 10 by 4 gives 2.5.

Keep practicing — related questions