Question

There is a total of 45 boys and girls in a choir.

The mean age of the 18 boys is 16.2 years.
The mean age of the 27 girls is 16.7 years.

Calculate the mean age of all 45 boys and girls.

Answer 1

The mean age of all 45 boys and girls is 16.5years

Explanation:

Since the mean age of the 18 boys is 16.2years,

∴ Sum of their ages = 18 × 16.2

= 291.6years

The mean age of the 27 girls is 16.7years

∴ Sum of their ages = 27 × 16.7

= 450.9years

∴ Mean age of all 45 boys and girls =
`(291.6 + 450.9)/(45)` years

=
`(742.5)/(45)` years

= 16.5 years

∴ The mean age of all 45 boys and girls is 16.5 years.

Answer 2

16.5 year

Explanation:

Using, mean = sum/no. *of observations

Here,

=> 16.2 = (sum of ages of boys)/18

=> 16.2 x 18 = sum of ages of boys

=> 291.6 = sum of ages of boys

Similarly, sum of ages of girls = 27 x 16.7 = 450.9

Mean(total) = (sumof agesof boys + girls)/45

Mean = (291.6 + 450.9)/45 = 16.5