Question

Calculate the standard deviation by :

(A) Actual mean method

(B) Direct method

(C) Short cut method.

3, 4, 6, 7, 10

Answer 1

$\begin{array}{ccc}\text{Actual mean method}& \text{Direct method}& \text{Short-cut method}\\ \overline{X}=\frac{\sum X}{N}=\frac{30}{5}=6& {\sigma }_X=\sqrt{\frac{\sum X^2}{N}}-(\overline{X}{)}^2& {\sigma }_X=\sqrt{\frac{\sum d^2}{N}-{\left(\frac{\sum d}{N}\right)}^2}\\ {\sigma }_X=\sqrt{\frac{\sum x^2}{N}}=\sqrt{\frac{30}{5}}=\sqrt{6}=2.45& =\sqrt{\frac{210}{5}-(6{)}^2}=\sqrt{6}=2.45& =\sqrt{\frac{30}{5}-{\left(\frac{0}{5}\right)}^2}=\sqrt{6}=2.45\end{array}$