Question

The mean of 5 numbers is 10, and their variance is 16. If one number is increased by 5, what is the new mean?

• A. 10
• B. 11
• C. 12
• D. 13

Hint:

To find the new mean after altering one data point, adjust the sum by the change and divide by the number of data points.

Answer 1

The Correct Option is B

The mean of 5 numbers is 10, so their sum is: \[ 5 \cdot 10 = 50 \] If one number is increased by 5, the new sum is: \[ 50 + 5 = 55 \] The new mean for 5 numbers is: \[ \text{New mean} = \frac{55}{5} = 11 \] (Note: Variance is not needed to calculate the new mean, as it only affects the spread, not the sum.) Thus, the new mean is: \[ \boxed{11} \]