The average of ten numbers is 7. If each number is multiplied by 12, then the average of the new set of number

Question

The average of ten numbers is 7. If each number is multiplied by 12, then the average of the new set of numbers will be:

Examoogle · Accepted Answer

The correct answer is Option B: 84. When every term in a set is multiplied by a constant 'k', the new average is simply the old average multiplied by that same constant 'k'. Here, 7 × 12 = 84.

Step-by-Step Solution & Concepts:
Shortcut Trick: When every term in a set is multiplied by a constant 'k', the new average is simply the old average multiplied by that same constant 'k'. Here, 7 × 12 = 84.

Formula Used: $$A_{new} = A_{old} 	imes k$$

Given: The average of ten numbers is 7. Each number is multiplied by 12.

Steps: Identify given average: The original average of the 10 numbers is given as 7.. Apply transformation rule: According to the properties of averages, if every number in a dataset is multiplied by a constant $k$, the average of the new set is the product of the original average and $k$. Here, $k = 12$.. Calculate the result: Multiplying the average by the constant yields the final value.

Answer: B is correct because multiplying each number by 12 results in the average being multiplied by 12, giving $7 	imes 12 = 84$.

Exam Tip: This property applies to all linear operations: if you add $c$ to each number, the average increases by $c$. If you multiply by $k$, the average is multiplied by $k$.

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