Question

The numbers of the book bought at a book fair by 200 students from a school are given in the following table.

$\begin{array}{cccccc}No.ofbooks& 0& 1& 2& 3& 4\\ No.ofstudents& 35& 64& 68& 18& 15\end{array}$

Calculate the standard deviation.

Answer 1

Let us take the assumed mean, A = 2

$\begin{array}{cccccc}x& f& d=x-a& d^2& fd& f{d}^2\\ 0& 35& -2& 4& -70& 140\\ 1& 64& -1& 1& -64& 64\\ 2\left(A\right)& 68& 0& 0& 0& 0\\ 3& 18& 1& 1& 18& 18\\ 4& 15& 2& 4& 30& 60\\ & \sum f=200& & & \sum fd=-86& \sum f{d}^2=282\end{array}$

$\sigma =\sqrt{\frac{\sum f{d}^2}{\sum f}-(\frac{\sum fd}{\sum f}{)}^2}=\sqrt{\frac{282}{200}-(\frac{-86}{200}{)}^2}=\sqrt{1.41-0.1849}$
$=\sqrt{1.2251}=1.1068=1.1$