Given below is the observed data of the ages of various children.

Age in years	Number of children
6	8
7	3
8	7
9	2
10	20

What is the mean of the ages of the children?

The correct option is 8.575 years.

To find the mean age of the children, we use the formula for the mean of a frequency distribution:

$\text{Mean}=\frac{\sum f_i{x}_i}{\sum f_i}$

where $x_i$ represents the age in years, and $f_i$ represents the number of children (frequency) for that age.

Step 1: Calculate the product of age and frequency ($f_i{x}_i$) for each category:

• Age 6: $6\times 8=48$
• Age 7: $7\times 3=21$
• Age 8: $8\times 7=56$
• Age 9: $9\times 2=18$
• Age 10: $10\times 20=200$

Step 2: Find the sum of all products ($\sum f_i{x}_i$):

$\sum f_i{x}_i=48+21+56+18+200=343$

Step 3: Find the total number of children ($\sum f_i$):

$\sum f_i=8+3+7+2+20=40$

Step 4: Calculate the mean:

$\text{Mean}=\frac{343}{40}=8.575\text{years}$

Thus, the mean age of the children is 8.575 years.