Question

The mean of the three numbers is $10.$ The mean of the other four numbers is $12.$
Find the mean of all the numbers.

Answer 1

Mean of three numbers $=\frac{\text{Sum of three numbers}}{3}$

$\Rightarrow 10=\frac{\text{Sum of three numbers}}{3}$ [$\because$ mean of three numbers $=10,$ given]

Hence, sum of three numbers $=30$

Mean of other four numbers $=\frac{\text{Sum of other four numbers}}{4}$

$\Rightarrow 12=\frac{\text{Sum of other four numbers}}{4}$ [$\therefore$ mean of other four numbers $=12,$ given]

Hence, sum of other four numbers $=48$

$\therefore$ Mean of all the numbers $=\frac{\text{Sum of all the numbers}}{\text{Total numbers}}$

$=\frac{\left[\text{Sum of first three numbers + Sum of other four numbers}\right]}{7}$

$=\frac{30+48}{7}=\frac{78}{7}=11.14$

Hence, mean of all the numbers is $11.14$