Effect of scaling on average: The average of 8 numbers is 21. If each number is multiplied by 8, what will be the average of the new set?

Introduction / Context:
This checks understanding that multiplying every value in a set by a constant multiplies the average by the same constant. The count does not change, so the mean scales directly.

Given Data / Assumptions:

• Average of 8 numbers = 21
• Each number is multiplied by 8

Concept / Approach:
If each x becomes 8x, then new average = 8 * old average. This follows from linearity of sums and the definition of mean.

Step-by-Step Solution:

Verification / Alternative check:
Let the original total be 21 * 8 = 168. After multiplying each by 8, the total becomes 168 * 8 = 1344. Dividing by the same count 8 gives 168 again.

Why Other Options Are Wrong:

• 8, 21, 29, 84: do not apply the constant scaling rule correctly.

Common Pitfalls:
Confusing operations on each member with operations on the average. Addition or multiplication across the set affects the mean identically.

Final Answer:
168