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. $11$

Answer 1

The correct option is C $22$

The given numbers are $12,23,34,45,56,67$ and $78$

Here, $n=7$ and sum $=315$

$\therefore Mean=\frac{315}{7}=45$

$\therefore$ Standard deviation

$=\sqrt{\frac{(12-45{)}^2+(23-45{)}^2+(34-45{)}^2+(45-45{)}^2+(56-45{)}^2+(67-45{)}^2+(78-45{)}^2}{7}}$

$=\sqrt{\frac{2(1089+484+121)}{7}}=\sqrt{\frac{3388}{7}}=\sqrt{484}=22$