Question

48 students were asked to write the total number of hours per week they spent on watching television. With this information find the standard deviation of hours spent on watching television.

$\begin{array}{cccccccc}x& 6& 7& 8& 9& 10& 11& 12\\ f& 3& 6& 9& 13& 8& 5& 4\end{array}$

• A. 1.6
• B. 2.6
• C. 3.2
• D. 3.8

Answer 1

The correct option is A 1.6

Mean
$\overline{x}=\frac{\sum x_i{f}_i}{N}=\frac{432}{48}=9$
($\because N=\sum f_i$)

$\begin{array}{cccccc}{x}_i& f_i& x_i{f}_i& d_i=x_i-\overline{x}& d_i^2& f_i{d}_i^2\\ 6& 3& 18& -3& 9& 27\\ 7& 6& 42& -2& 4& 24\\ 8& 9& 72& -1& 1& 9\\ 9& 13& 117& 0& 0& 0\\ 10& 8& 80& 1& 1& 8\\ 11& 5& 55& 2& 4& 20\\ 12& 4& 48& 3& 9& 36\\ & N=48& \sum x_i{f}_i=432& \sum d_i=0& & \sum f_i{d}_i^2=124\end{array}$

Standard Deviation
$\sigma =\sqrt{\frac{\sum f_i{d}_i^2}{N}}=\sqrt{\frac{124}{48}}=\sqrt{2.58}\approx 1.6$