Question

If each observation is multiplied by $\frac{1}{3}$ then the mean of the new data will de

• A. $\frac{1}{3}$ times
• B. 3 times
• C. $\frac{1}{\sqrt{3}}$ times
• D. $\frac{2}{3}$ times

Answer 1

Answer: (A)

$\frac{1}{3}$ times

Let set of data is 9,10,11,17 and 13

Then mean $=\frac{9+10+11+17+13}{5}=\frac{60}{5}$

If Each observation is multiply by $\frac{1}{3}$

Then data are $\frac{9}{3},\frac{10}{3},\frac{11}{3},\frac{17}{3}and\frac{13}{3}$

Then sum of data$=\frac{9}{3}+\frac{10}{3}+\frac{11}{3}+\frac{17}{3}+\frac{13}{3}=\frac{60}{3}=20$

Then new mean of data $=\frac{20}{5}=4$

Then new data mean $=\frac{4}{12}=\frac{1}{3}$ times of old data