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, $\sum _{i=1}^7{\left(x_i-\bar{x}\right)}^2$
$={\left(12-45\right)}^2+{\left(23-45\right)}^2+{\left(34-45\right)}^2+{\left(45-45\right)}^2+{\left(56-45\right)}^2+{\left(67-45\right)}^2+{\left(78-45\right)}^2$
$=1089+484+121+0+121+484+1089$
$=3388$
$\therefore \sigma =\sqrt{\frac{3387}{7}}=\sqrt{484}=22$