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
$=\sqrt{\frac{\begin{array}{rl}& {(12-45)}^2+{(23-45)}^2+{(34-45)}^2\\ & +{(45-45)}^2+{(56-45)}^2+{(67-45)}^2\\ & +{(78-45)}^2\end{array}}{7}}$
$=\sqrt{\frac{\begin{array}{rl}& {(33)}^2+{(22)}^2+{(11)}^2+0\\ & +{(11)}^2+{(22)}^2+{(33)}^2\end{array}}{7}}$
$=\sqrt{\frac{2(1089+484+121)}{7}}=\sqrt{\frac{3388}{7}}$
$=\sqrt{484}=22$