Question

Calculate the standard deviation for the following data :

$\begin{array}{cccccccc}Class:& 0-30& 30-60& 60-90& 90-120& 120-150& 150-180& 180-210\\ Frequency:& 9& 17& 43& 82& 81& 44& 24\end{array}$

Answer 1

$\begin{array}{ccccccc}CI& f_i& x_i& u_i=(x_i-A)/h& f_i{u}_i& u_i^2& f_i{u}_i^2\\ 0-30& 9& 15& -3& -27& 9& 81\\ 30-60& 17& 45& -2& -34& 4& 68\\ 60-90& 43& 75& -1& -43& 1& 43\\ 90-120& 82& 105& 0& 0& 0& 0\\ 120-150& 81& 135& 1& 81& 1& 81\\ 150-180& 44& 165& 2& 88& 4& 176\\ 180-210& 24& 195& 3& 72& 9& 216\\ & 300& & & 137& & 665\end{array}$

Here, N = 300, A = 105 , $\sum f_i{u}_i=137,\sum f_i{u}_i^2=665andh=35$

$\therefore Mean=\overline{x}=A+h(\frac{1}{N}\sum f_i{u}_i)$

$\Rightarrow \overline{x}=105+30\left(\frac{137}{300}\right)=118.7$

$var\left(x\right)=h^2[\frac{1}{N}\sum f_i{u}_i^2-{(\frac{1}{N}\sum f_i{u}_i)}^2]=900,[\frac{665}{300}-{\left(\frac{137}{300}\right)}^2]=1807.31$

$\therefore S.D=\sqrt{var\left(x\right)}=\sqrt{1807.31}=42.51$