Question

Some households in a society are sorted according to their electricity usage and given in the table below :

$\begin{array}{cc}\text{Usage of electricity (units)}& \text{No. of households}\\ 80-90& 4\\ 90-100& 6\\ 100-110& 5\\ 110-120& 8\\ 120-130& 7\\ 130-140& 3\end{array}$

Find the median usage

• A. 112
• B. 111.25
• C. 112.5
• D. 111.875

Answer 1

The correct option is D

111.875

$\begin{array}{cc}\text{Usage of electricity (units)}& \text{No. of households}\\ \text{Below}90& 4\\ \text{Below}100& 10\\ \text{Below}110& 15\\ \text{Below}120& 23\\ \text{Below}130& 30\\ \text{Below}140& 33\end{array}$

Number of households (n) = 33

Median will be $(\frac{n+1}{2}{)}^{th}$ term = 17th term.

17th term lies in 110-120 range and there are 8 values in that range

The values from 16th term to 23rd term will be an increase from 110 by $\frac{5}{4}$ or 1.25

17th term will lie between 111.25 and 112.50

$\therefore$ Median = 17th term = $\frac{111.25+112.50}{2}$ = 111.875