Question

The age of 30 workers in a factory are as follows

$\begin{array}{cc}\text{Age}& \text{No. of workers}\\ 24& 5\\ 25& 7\\ 26& 8\\ 27& 4\\ 28& 6\end{array}$

(i) Find the mean,median and mode for the above ungrouped data. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark each

$\begin{array}{ccc}\text{Age}& \text{No. of workers}& fx\\ 24& 5& 120\\ 25& 7& 175\\ 26& 8& 208\\ 27& 4& 108\\ 28& 6& 168\end{array}$

Mean
$=\frac{\sum fx}{\sum f}=\frac{(24\times 5)+(25\times 7)+(26\times 8)+(27\times 4)+(28\times 6)}{5+7+8+4+6}$

$=\frac{779}{30}$

$=25.97$
$\begin{array}{ccc}\text{Age}& \text{No of Workers}& \text{C.F}\\ 24& 5& 5\\ 25& 7& 12\\ 26& 8& 20\\ 27& 4& 24\\ 28& 6& 30\end{array}$

Median $=\frac{{\left(\frac{n}{2}\right)}^{th}observation+{(\frac{n}{2}+1)}^{th}observation}{2}$

$=\frac{{15}^{th}observation+{16}^{th}observation}{2}$

$=\frac{26+26}{2}$

$=26$

Highest frequency = 8

Mode = 26