The average of 7 numbers is 53. If each number is increased by 6, what will the new average be?

Correct option is D

Given:

The average of 7 numbers is 53. If each number is increased by 6, what will the new average be?

Formula used:

​$$\text{Average} = \frac{\text{Sum of the numbers}}{\text{Number of numbers}}$$​​

Solution: 

The average of 7 numbers is calculated by: 

​$$\text{Average} = \frac{\text{Sum of the numbers}}{\text{Number of numbers}}$$​​

Let the sum of the 7 numbers be $S$. Since the average is 53, we can write

​$$\frac{S}{7} = 53$$ 

$$S = 53 \times 7 = 371$$​​

So, the sum of the 7 numbers is 371.

If each number is increased by 6, the total increase for all 7 numbers is

7 × 6 = 42 

Therefore, the new sum of the numbers becomes:

​$$S_{\text{new}} = S + 42 = 371 + 42 = 413$$​​

Now, we calculate the new average by dividing the new sum by 7:

​$$\text{New average} = \frac{S_{\text{new}}}{7} = \frac{413}{7} = 59$$​​

Thus, the new average is 59.​