Question

The mean of twenty observations $x_1,x_2,x_3,x_4,...x_{20}$ is $m$. If each of the first ten observations is increased by 8 and each of the next 10 observations is decreased by 8, then the new mean is $n$. The difference $m-n$ equals

• A. $16$
• B. $20$
• C. $0$
• D. $8$

Answer 1

The correct option is C $0$

Mean is the sum of the data values divided by the total number of data values.

Given that mean of $20$ observations $x_1,x_2,...,x_{20}$ is $m$

$⟹m=\frac{x_1+x_2+x_3+...+x_{20}}{20}$ ------(1)

New mean after increasing first ten numbers by 8 and decreasing next ten numbers by 8 is $n$

$⟹n=\frac{x_1+8+x_2+8+....+x_{10}+8+x_{11}-8+...+x_{20}-8}{20}$

$⟹n=\frac{x_1+x_2+x_3+...+x_{20}}{20}$ ------(2)

subtracting (1) and (2) we get

$m-n=\frac{x_1+x_2+...+x_{20}}{20}-\frac{x_1+x_2+...+x_{20}}{20}$

$⟹m-n=0$