Average of eight numbers is 12. If each number is increased by 2, then average of new numbers is :

Question

Accepted Answer

To solve the problem, we need to understand how the average of a set of numbers changes when each number in the set is increased by a constant amount.

1. **Initial Average Calculation:**
   - The average of eight numbers is given as 12. 
   - This means the sum of these eight numbers is $8 \times 12 = 96$.

2. **Effect of Increasing Each Number by 2:**
   - If each of the eight numbers is increased by 2, the new numbers will be the original numbers plus 2.
   - Therefore, the sum of the new numbers will be $96 + (8 \times 2) = 96 + 16 = 112$.

3. **New Average Calculation:**
   - The average of the new numbers is the sum of the new numbers divided by the number of numbers, which is still 8.
   - So, the new average is $\frac{112}{8} = 14$.

Thus, the average of the new numbers is 14, which corresponds to Option 4.

**Explanation of Why Other Options are Incorrect:**

- **Option 1 (13):** 
  - This option suggests that the average increases by 1 when each number is increased by 2. However, since each of the eight numbers is increased by 2, the total increase in the sum is 16, leading to an increase in the average by 2, not 1.

- **Option 2 (12):**
  - This option implies that the average remains unchanged even after increasing each number by 2. This is incorrect because increasing each number by a positive amount will increase the overall average.

- **Option 3 (15):**
  - This option suggests that the average increases by 3. However, as calculated, the increase in the average is exactly 2, not 3, because the total increase in the sum is 16, which when divided by 8 gives an increase of 2.

Therefore, the correct answer is Option 4, which accurately reflects the new average as 14.