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  4. The mean height of 36 boys in a cricket academy is 160 mathrm~cm, and the mean height of 24 girls in the same academy is 155 mathrm~cm. The combined mean height of 60 students in the cricket academy is (in mathrmcm ).

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Q. The mean height of $36$ boys in a cricket academy is $160 \mathrm{~cm}$, and the mean height of $24$ girls in the same academy is $155 \mathrm{~cm}$. The combined mean height of $60$ students in the cricket academy is___ (in $\mathrm{cm}$ ).

Statistics

Solution:

Given: $n_1=36, n_2=24$
$\overline{x_1}=172, \overline{x_2}=160$
Combined mean,
$\bar{x} =\frac{n_1 \overline{x_1}+n_2 \overline{x_2}}{n_1+n_2}=\frac{36 \times 160+24 \times 155}{36+24} $
$ =\frac{9480}{60}=158$