Question

If the mean of a set of observations $x_1,x_2,...x_{10}$ is $20$ then the mean of $x_1+4,x_2+8,x_3+12,...x_{10}+40$ is?

• A. $34$
• B. $42$
• C. $38$
• D. $40$

Answer 1

Answer: (B)

$42$

$\overline{x}=\frac{x_1+x_2+x_3+.....+x_{10}}{N}=\frac{\sum x_n}{N}=20=\frac{{\sum }_n}{10}$

So, $\sum x_n=200$

Now, New $\overline{x}=\frac{x_1+x_2+8+....+x_{10}+40}{N}$

New $\overline{x}=\frac{\sum x_n+4(1+2+3+....+10)}{10}=42$