Question

The mean of a set of 10 numbers is 60. When a number x is added to the set, the mean is changed to 65.

Find the value of x.
x =

Answer 1

To find the value of x for a set of numbers whose mean increases from 60 to 65 after adding x, subtract the total sum of the 10 original numbers (600) from the total sum with the added number (715), which gives x = 115.

Step-by-step explanation:

The mean of a set of 10 numbers is 60. This implies that the total sum of these 10 numbers is 10 × 60, which equals 600. When an additional number, x, is added to the set, the new mean of the 11 numbers becomes 65. This indicates that the sum of the 11 numbers is 11 × 65, yielding a total of 715. To find the value of x, we subtract the original sum (600) from the new sum (715).

Calculating the value of x:

1. Original sum of 10 numbers = 10 × 60 = 600
2. New sum of 11 numbers = 11 × 65 = 715
3. Subtract the original sum from the new sum: 715 - 600 = 115
4. The value of x is 115.