The average of 8 numbers is 45. If each number is increased by 4, what will…

Concept

When the same constant is added to every observation, the average increases by that constant. This follows because the total increases by the constant multiplied by the number of observations, and dividing by that count leaves the same constant.

Application

1. The original average is 45.

2. Every number is increased by 4, so the new average is 45 + 4 = 49.

Cross-check

1. The original total of 8 numbers is 8 × 45 = 360.

2. Increasing all 8 numbers by 4 adds 8 × 4 = 32, so the new total is 360 + 32 = 392.

3. The new average is 392 ÷ 8 = 49, confirming the result.