Question

Find the mean of the data given in the table using step - deviation method.
$\begin{array}{cc}\text{Class Interval}& \text{Frequency}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 7\\ 30-40& 6\\ 40-50& 5\\ 50-60& 8\end{array}$

Answer 1

$\begin{array}{ccccc}\text{Class Internal}& \text{Mid value}\left(x_i\right)& \text{Frequency}\left(f_i\right)& u=\frac{x_i-a}{h}& f_i{u}_i\\ 0-10& 5& 10& -3& -30\\ 10-20& 15& 12& -2& -24\\ 20-30& 25& 7& -1& -7\\ 30-40& 35=a& 6& 0& 0\\ 40-50& 45& 5& 1& 5\\ 50-60& 55& 8& 2& 16\\ \text{Total}& & \sum f_i=48& \sum u=-3& \sum f_i{u}_i=-40\end{array}$

Let the assumed mean (a) = 35.
Class width (h) = 10 - 0 = 10

$\therefore Mean=a+\frac{\sum f_i{u}_i}{\sum f_i}\times h$

$=35+\frac{-40}{48}\times 10$

$=35+(-8.33)$

$=35-8.33$

$=26.67$