The average of 11 numbers is 7. If every number is doubled, what will be the new average of these 11 numbers?

Introduction / Context:
This is a basic concept check on how averages behave under scaling operations. The question asks what happens to the average if each number in the set is multiplied by a constant factor, in this case doubled.

Given Data / Assumptions:
- There are 11 numbers. - Their average is 7. - Each of the 11 numbers is doubled. - We must find the new average after doubling every number.

Concept / Approach:
Average equals total sum divided by number of terms. When each term is multiplied by a constant k, the total sum is also multiplied by k, while the number of terms stays the same. Therefore, the new average is simply k times the old average. Here k is 2 because we double each number.

Step-by-Step Solution:
Step 1: Let the 11 numbers be n1, n2, ..., n11. Step 2: Their sum S satisfies S / 11 = 7, so S = 7 * 11 = 77. Step 3: After doubling, each number becomes 2n1, 2n2, ..., 2n11. Step 4: New total sum S new = 2n1 + 2n2 + ... + 2n11 = 2(n1 + ... + n11) = 2S. Step 5: Hence S new = 2 * 77 = 154. Step 6: New average = S new / 11 = 154 / 11 = 14.

Verification / Alternative check:
Use the scaling property directly. Since each number is multiplied by 2, the average must also be multiplied by 2. Old average = 7, so new average = 2 * 7 = 14. This agrees with the detailed calculation and confirms the reasoning.

Why Other Options Are Wrong:
- 3.5 is obtained by halving instead of doubling. - 7 is the original average and ignores the change. - 10.5 and 21 come from incorrect or random multipliers applied to the original average.

Common Pitfalls:
Learners sometimes confuse operations on each term with operations on the number of terms, or they try to recalculate with assumed values. Remember that scaling every term by the same constant scales the average by exactly that constant. This rule saves time in many aptitude questions.

Final Answer:
The new average of the numbers is 14.