Question

The mean height of 9 girls and 11 boys is 163.75 cm.If the mean height of the 11 boys is 166 cm,find the mean height of the 9 girls

Answer 1

Answer: The mean height of 9 girls is 161 cm.

Explanation:

Let the heights of girls and boys are represented by

$x_i\text{ and }y_i\text{ respectively}$

Since we have given that

the mean height of 9 girls and 11 boys is 163.75 cm

so, equation (1)

$\frac{\sum x_i+\sum y_i}{9+11}=163.75\\\\\sum x_i+\sum y_i=163.75\times 20\\\\\sum x_i+\sum y_i=3275$

Similarly,

the mean height of 11 boys =166 cm

so, equation (2)

$\frac{\sum y_i}{11}=166\\\\\sum y_i=166\times 11\\\\\sum y_i=1826$

if we put the value of equation (2) in equation (1),

$\sum x_i+1826=3275\\\\\sum x_i=3275-1826\\\\\sum x_i=1449$

So, the mean height of 9 girls is given by

$\frac{\sum x_i}{9}=\frac{1449}{9}=161\text{ cm}$