Question

Find the mean using step-deviation.

$\begin{array}{cc}ClassInterval& Frequency\\ 0-10& 160\\ 10-20& 200\\ 20-30& 320\\ 30-40& 480\\ 40-50& 300\\ 50-60& 140\end{array}$ [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Let the assumed mean be 25

Class size = 10

$\begin{array}{ccccc}{x}_i& f_i& d_i& u_i& f_i{u}_i\\ \text{5}& \text{16}& \text{-20}& \text{-2}& \text{-32}\\ \text{15}& \text{20}& \text{-10}& \text{-1}& \text{-20}\\ \text{25}& \text{32}& \text{0}& \text{0}& \text{0}\\ \text{35}& \text{48}& \text{10}& \text{1}& \text{48}\\ \text{45}& \text{30}& \text{20}& \text{2}& \text{60}\\ \text{55}& \text{14}& \text{30}& \text{3}& \text{42}\end{array}$

$\sum f_i=160$

$\sum f_i{u}_i=98$

Mean
$=25+(\frac{98}{160}\times 10)$

$=25+6.125$

$=31.125$