Question

Find the standard deviation of $12, 23,34, 45,56, 67$ and $78$.

• A. $2$
• B. $4$
• C. $22$
• D. $11$

Answer 1

Answer: (C)

Standard deviation of ungrouped data is,
$ \sigma = \sqrt{\frac{\sum\left(x_{i}-\bar{x}\right)^{2}}{n}} $
Here, $\bar{x} =\frac{ 12+23+34+45+56+67+78}{7} = 45 $
Now, $\sum\limits_{i=1}^{7} \left(x_{i}-\bar{x}\right)^{2}$
$ = \left(12-45\right)^{2} +\left(23-45\right)^{2}+\left(34-45\right)^{2} + \left(45-45\right)^{2} +\left(56-45\right)^{2} +\left(67-45\right)^{2}+\left(78-45\right)^{2} $
$ = 1089+484+121+0+121+484+1089 $
$= 3388$
$ \therefore \sigma = \sqrt{\frac{3387}{7}} = \sqrt{484} = 22$