Question

The standard deviation for the scores $1, 2, 3, 4, 5, 6$ and $7$ is $2$. Then, the standard deviation of $12, 23, 34, 45, 56, 67$ and $78$ is

• A. 2
• B. 4
• C. 22
• D. 11
• E. 44

Answer 1

Answer: (C)

Here, $ n=7, $ sum =315 Now, Mean
$=\frac{315}{7}=45 $
$ \therefore $ Standard deviation
$=\sqrt{\frac{\begin{align} & {{(12-45)}^{2}}+{{(23-45)}^{2}}+{{(34-45)}^{2}} \\ & +{{(45-45)}^{2}}+{{(56-45)}^{2}}+{{(67-45)}^{2}} \\ & +{{(78-45)}^{2}} \\ \end{align}}{7}} $
$=\sqrt{\frac{\begin{align} & {{(33)}^{2}}+{{(22)}^{2}}+{{(11)}^{2}}+0 \\ & +{{(11)}^{2}}+{{(22)}^{2}}+{{(33)}^{2}} \\ \end{align}}{7}} $
$=\sqrt{\frac{2(1089+484+121)}{7}}=\sqrt{\frac{3388}{7}} $
$=\sqrt{484}=22 $