Question

Mean of $10$ observations is $50$ and their standard deviation is $10$. If each observation is subtracted by $5$ and then divided by $4$, then the new mean and standard deviation are

• A. 22.5, 2.5
• B. 11.25, 2.5
• C. 11.5, 2.5
• D. 11, 2.5
• E. 11.75, 2.5

Answer 1

Answer: (B)

Given,
Mean of 10 observations $=\frac{\displaystyle\sum_{i=1}^{10} x_{i}}{10}=50$
$\Rightarrow \, \displaystyle\sum_{i=1}^{10} x_{i}=500\,\,\,\,\,\dots(i)$
$\therefore $ New mean $=\frac{\displaystyle\sum_{i=1}^{10} x_{i}-5 \times 10}{4 \times 10}=\frac{500-50}{4 \times 10}$
[using Eq. (i)]
$=\frac{450}{4 \times 10}=11.25$
and standard deviation $=\frac{\text { old }( SD )}{4}=\frac{10}{4}=2.5$