Question

If each observation of a data is increased by 5, then their mean

• A. Is decreased by 5
• B. Is increased by 5
• C. Becomes 7 times the original mean
• D. Remains the same.

Answer 1

The correct option is B

Is increased by 5

Let $\overline{x}=\frac{x_1+x_2+\dots \dots +x_n}{n}$
If 5 is added in each observation, then
Mean $=\frac{(x_1+5)+(x_2+5)+\dots \dots +(x_n+5)}{n}$
$=\frac{(x_1+\dots \dots +x_n)+5n}{n}=\overline{x}+5$