Question

The amount of rainfall in a particular season for 5 days are given as 10 cm, 12 cm, 14 cm, 16 cm and 8 cm Find it's standard deviation using mean method.

• A. 2.83
• B. 5.25
• C. 3.26
• D. 4.15

Answer 1

The correct option is A 2.83

Arranging the numbers in ascending order, use get, 8, 10, 12, 14, 16.

Mean
$=\frac{8+10+12+14+16}{5}=\frac{60}{5}=12$

$\begin{array}{ccc}xi& di=xi-\overline{x}=xi-12& d{i}^2\\ 8& -4& 16\\ 10& -2& 4\\ 12& 0& 0\\ 14& 2& 4\\ 16& 4& 16\\ & & \sum d{i}^2=40\end{array}$

Standard Deviation

$\sigma =\sqrt{\frac{\sum d{i}^2}{n}}$

$=\sqrt{\frac{40}{5}}=\sqrt{8}\simeq 2.83$