The average of ten numbers is 7. If each number is multiplied by 12, then the…
2024
The average of ten numbers is 7. If each number is multiplied by 12, then the average of the new set of numbers is:
- A.
42
- B.
84
- C.
82
- D.
19
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept: The average of a set of numbers equals the sum of the numbers divided by their count. Averaging is a linear operation, so if every number in a set is scaled by a constant factor k, the sum scales by k as well, and therefore the average scales by exactly k too — recomputing the full set is never necessary.
The average of the ten numbers is 7, so their total sum = 7 × 10 = 70.
Each of these ten numbers is multiplied by 12, so the new sum = 70 × 12 = 840.
New average = new sum ÷ count = 840 ÷ 10 = 84.
Cross-check: Using the scaling property directly, new average = original average × scaling factor = 7 × 12 = 84, which matches the sum-based calculation above.
Therefore, the average of the new set of numbers is 84.