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

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,

$\overline{X}_{12}=\dfrac{n_1\overline{X}_1+n_2\overline{X}_2}{n_1+n_2}$

After substituting the given values, we get

$16=\dfrac{21(14)+14\overline{X}_2}{21+14}$

$16=\dfrac{294+14\overline{X}_2}{35}$

$16\times 35=294+14\overline{X}_2$

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

On further simplification, we get

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

$266=14\overline{X}_2$

$\dfrac{266}{14}=\overline{X}_2$

$19=\overline{X}_2$

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