Question

20 students were asked to write the number of hours they spent per week on studies. With the given information find the standard deviation of the number of hours spent using Mean method.

$\begin{array}{ccccc}{x}_i& 2& 4& 5& 10\\ f_i& 5& 10& 4& 1\end{array}$

• A. 1.73
• B. 2.24
• C. 3.75
• D. 4.29

Answer 1

The correct option is A 1.73

$\frac{Mean}{x}=\frac{\sum xifi}{N}=\frac{80}{20}=4$
$\begin{array}{cccccc}xi& fi& xifi& di=xi-\overline{x}& d{i}^2& fid{i}^2\\ 2& 5& 10& -2& 4& 20\\ 4& 10& 40& 0& 0& 0\\ 5& 4& 20& 1& 1& 4\\ 10& 1& 10& 6& 36& 36\\ & n=20& \sum xifi=80& \sum di=5& & \sum fid{i}^2=60\end{array}$

Standard Deviation

$\sigma =\sqrt{\frac{\sum fid{i}^2}{N}}=\sqrt{\frac{60}{20}}=\sqrt{3}=1.73$