Question

There are 21 boys and 14 girls in a hall, each holding coins in their hand.The mean number of coins for the children is 16

The mean number of coins for the boys is 14
Work out the mean number of coins for the girls.

Answer 1

Given:

Number of boys = 21

Number of girls = 14

Mean number of coins for the children = 16

Mean number of coins for the boys = 14

To find:

The mean number of coins for the girls.

Solution:

We have,

`n_1=21`

`n_2=14`

`\overline{X}_(12)=16`

`\overline{X}_1=14`

We need to find the value of
`\overline{X}_2`.

We know that,

`\overline{X}_(12)=\frac{n_1\overline{X}_1+n_2\overline{X}_2}{n_1+n_2}`

After substituting the given values, we get

`16=\frac{21(14)+14\overline{X}_2}{21+14}`

`16=\frac{294+14\overline{X}_2}{35}`

`16* 35=294+14\overline{X}_2`

`560=294+14\overline{X}_2`

On further simplification, we get

`560-294=14\overline{X}_2`

`266=14\overline{X}_2`

`(266)/(14)=\overline{X}_2`

`19=\overline{X}_2`

Therefore, the mean number of coins for the girls is 19.