Question

the average age of a group of 9 children is 15 years and that of a group of a group og 7 children is 13 years.find the average age of the group of the 16 boys.​

Answer 1

$\large\underline{\sf{Given- }}$

Group 1

$\rm :\longmapsto\:Number \: of \: children, \: n_1 = 9$

$\rm :\longmapsto\:Average \: age \: of \: children, \:\overline{x_1} = 15 \: years$

Group 2

$\rm :\longmapsto\:Number \: of \: children, \: n_2 = 7$

$\rm :\longmapsto\:Average \: age \: of \: children, \:\overline{x_2} = 13 \: years$

So,

$\rm :\longmapsto\:\sf \: Let \: average \: age \: of \: 16 \: children \: be \: X \: years$

Average age of 16 children is given by

$\rm :\longmapsto\:X = \dfrac{n_1 \: \overline{x_1} \: + \: n_2 \: \overline{x_2}}{n_1 \: + \: n_2}$

$\rm :\longmapsto\:X = \dfrac{15 \times 9 + 13 \times 7}{9 + 7}$

$\rm :\longmapsto\:X = \dfrac{135 \: + \: 91}{16}$

$\rm :\longmapsto\:X = \dfrac{226}{16}$

$\rm :\longmapsto\:X = 14.125$

Additional Information :-

$\boxed{ \sf \: \sf \:Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations}}$

• 1. If there are n observations having mean X, then mean is also increased by k, if each observation is increased by k.

• 2. If there are n observations having mean X, then mean is also decreased by k, if each observation is decreased by k.

• 3. If there are n observations having mean X, then mean is also multipllied by k, if each observation is multiplied by k.

• 4. The sum of deviations taken from mean is zero.