Question

The mean of the ages of 13 children is 6. What would be the mean of their ages after 4 years?

• A. 11
• B. 12
• C. 10
• D. 13

Answer 1

The correct option is C 10

Mean of 13 children is 6.
After 4 years, ages of all children will increase by 4.
Since all values are shifted by the same amount, the measures of the mean is also shifted by the same amount. If 4 is added to each data value, the mean will also increase by 4.
Thus, mean of children ages after 4 years is 6 + 4 = 10.
Alternative Method

According to question,
Mean = $\frac{Sumofagesofchildern}{Numberofstudents}$
6 = $\frac{Sumofagesofchildern}{13}$
Sum of ages of childern = 13 $\times$ 6 = 78

After 4 years, ages of all children will be increased by 4.
So, after 4 years, sum ages of children = 13 $\times$ 4 + 78 = 130
New Mean = $\frac{Sumofagesofchildernafter4years}{Numberofstudents}$
= $\frac{130}{13}$ = 10
Thus, mean of children ages after 4 years is 10.