Question

Find the mean using step-deviation.
$\begin{array}{cc}ClassInterval& Frequency\\ 35-45& 200\\ 45-55& 250\\ 55-65& 50\\ 65-75& 70\\ 75-85& 40\end{array}$

Answer 1

Let the assumed mean be 60.

Class size h = 10

$\begin{array}{ccccc}{x}_i& f_i& d_i=x_i-60& u_i=d_i/h& f_i{u}_i\\ \text{40}& \text{200}& \text{-20}& \text{-2}& \text{-400}\\ \text{50}& \text{250}& \text{-10}& \text{-1}& \text{-250}\\ \text{60}& \text{50}& \text{-0}& \text{0}& \text{0}\\ \text{70}& \text{70}& \text{10}& \text{1}& \text{70}\\ \text{80}& \text{40}& \text{20}& \text{2}& \text{80}\end{array}$

$\sum f_i=610$

$\sum f_i{u}_i=-500$

Mean= a + $\frac{\sum f_i{u}_i}{\sum f_i}\times h$
$=60+(\frac{-500}{610}\times 10)$

$=60-8.20$

$=51.80$