Question

The mean of ten numbers is $\text{14}$. Four of the numbers have a mean of $\text{10}$.The remaining six numbers are$\text{16,20,22,x,8 and 10}$.

Find the sum of the remaining six numbers.

Answer 1

Step 1: Find the sum of four numbers.

Finding the sum of six numbers

Mean of $\text{10}$ numbers is $\text{14}$

Four number mean is $\text{10}$

$\frac{{\text{x}}_1+x_2+x_3+x_4}{\text{4}}\text{= 10}$

${\text{x}}_1{\text{+x}}_2{\text{+x}}_3{\text{+x}}_4\text{=40}$……………(1)

Step 2: Find the value of $x$

The mean of $10$ numbers $=14$(given)

$\frac{{\text{x}}_{\text{1}}{\text{+x}}_2{\text{+x}}_3{\text{+x}}_4\text{+16+20+22+x+8+10}}{\text{10}}\text{=14}$

From (1)

$\frac{\text{40+16+20+22+x+8+10}}{\text{10}}\text{=14}$

$\text{x = 24}$

Step 3: Find the sum of six numbers.

Sum of the six numbers $\text{= 16+20+22+24+8+10}$

$\text{=100}$

Hence the sum of the remaining six numbers is $\text{100}$.