Question

The mean of 7 numbers is 20. If three numbers are included but there is no change in the mean, then the mean of included numbers is

• A. 17
• B. 18
• C. 19
• D. 20

Answer 1

The correct option is D 20

Let 7 numbers be $x_1,x_2,x_3,....,x_7.$
Given that the mean of 7 numbers is 20.
$\therefore \frac{x_1+x_2+...+x_7}{7}=20$
$\Rightarrow x_1+x_2+...+x_7=7\times 20$
= 140 ........(i)
Let the three numbers included be a, b and c.
Thus, 20 = $\frac{(x_1+x_2+...+x_7)+a+b+c}{10}$ (No change is mean)
$\Rightarrow 20\times 10=140+(a+b+c)$ [From (i)]
$\Rightarrow 200=140+(a+b+c)$
$\Rightarrow 60=a+b+c$
∴ Mean of (a, b, c) =$\frac{a+b+c}{3}$
$=\frac{60}{3}$
= 20
Hence, the correct answer is option (d).