Question

Question 15
Weekly income of 600 families is tabulated below ?
$\begin{array}{cc}Weeklyincome\left(inRs\right)& Numberoffamilies\\ 0-1000& 250\\ 1000-2000& 190\\ 2000-3000& 100\\ 3000-4000& 40\\ 4000-5000& 15\\ 5000-6000& 5\\ Total& 600\end{array}$
Compute the median income.

Answer 1

First we construct a cumulative frequency table.
$\begin{array}{ccc}Weeklyincome\left(inRs\right)& Numberoffamilies\left(f_i\right)& Cumulativefrequency\left(c_f\right)\\ 0-1000& 250& 250\\ 1000-2000& 190& 250+190=440\\ 2000-3000& 100& 440+100=540\\ 3000-4000& 40& 540+40=580\\ 4000-5000& 15& 580+15=595\\ 5000-6000& 5& 595+5=600\end{array}$
It is given that, n = 600
$\therefore \frac{n}{2}=\frac{600}{2}=300$
The cumulative frequency greater than 300=440 that lies in the interval 1000-2000.
so median class=1000-2000
Here, (lower limit) $l=1000$
$f\left(frequencyofmedianclass\right)=190c_f\left(cumulativefrequencyofclassprecedingmedianclass\right)=250\left(classwidth\right)h=1000and\left(totalobservation\right)n=600\therefore Median=l+(\frac{\{\frac{n}{2}-c_f\}}{f}\times h)=1000+\frac{(300-250)}{190}\times 1000=1000+\frac{50}{190}\times 1000=1000+\frac{5000}{19}=1000+263.15=1263.15$
Hence, the median income Rs 1263.15.