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,
[tex]n_1=21[/tex]
[tex]n_2=14[/tex]
[tex]\overline{X}_{12}=16[/tex]
[tex]\overline{X}_1=14[/tex]
We need to find the value of [tex]\overline{X}_2[/tex].
We know that,
[tex]\overline{X}_{12}=\dfrac{n_1\overline{X}_1+n_2\overline{X}_2}{n_1+n_2}[/tex]
After substituting the given values, we get
[tex]16=\dfrac{21(14)+14\overline{X}_2}{21+14}[/tex]
[tex]16=\dfrac{294+14\overline{X}_2}{35}[/tex]
[tex]16\times 35=294+14\overline{X}_2[/tex]
[tex]560=294+14\overline{X}_2[/tex]
On further simplification, we get
[tex]560-294=14\overline{X}_2[/tex]
[tex]266=14\overline{X}_2[/tex]
[tex]\dfrac{266}{14}=\overline{X}_2[/tex]
[tex]19=\overline{X}_2[/tex]
Therefore, the mean number of coins for the girls is 19.
