Effect of scaling on averages: The average of ten numbers is 7. If each number is multiplied by 12, what is the average of the new numbers?

Introduction / Context:
Multiplying every term in a dataset by a constant scales the average by the same constant.

Given Data / Assumptions:

• Initial average = 7
• Scaling factor = 12

Concept / Approach:
If each value becomes 12 * value, then average becomes 12 * average.

Step-by-Step Solution:

Verification / Alternative check:
Let the total initially be T = 10 * 7 = 70. After scaling, total = 12 * 70 = 840. New average = 840 / 10 = 84. Matches.

Why Other Options Are Wrong:

• 7 and 9: Ignore scaling property.
• 82: Arbitrary and unsupported by the constant factor rule.

Common Pitfalls:
Trying to add instead of multiply the average or confusing the constant's effect.

Final Answer: