Question

Q. 13. Weekly income of 600 families is tabulated below :
Weekly income (in F.) Number of families
250
190
0-1000
1000-2000
2000-3000
3000-4000
4000-5000
5000-6000
100
40
15
5
Total
600
Compute the median income.​

Answer 1

Step-by-step explanation:

Given that:

Weekly income of 600 families is tabulated below :

Weekly income (in F.) Number of families

0-1000

1000-2000

2000-3000

3000-4000

4000-5000

5000-6000

250

190

100

40

15

5

Total

600

To find:Compute the median income

Solution: To find the median income first we have to find cumulative frequency.

For that tabulate the given data

$\begin{tabular}{|c|c|c|c|}\cline{1-3}Weekly\:income(inF.)& Number\:of\: families(f_i)& Cumulative\:frequency(CF)\\\cline{1-3}0-1000&250&250\\\cline{1-3}1000-2000&190&440\\\cline{1-3}2000-3000&100&540\\\cline{1-3}3000-4000&40&580\\\cline{1-3}4000-5000&15&595\\\cline{1-3}5000-6000&5&600\\\cline{1-3}Total&600\\\cline{1-3}\end{tabular}$

$\boxed{Median:= l + \bigg( \frac{ \frac{n}{2} - cf}{f}\bigg) \times h}$

here

l= Lower limit of Median class

n/2=Total frequency divided by 2

cf: Cumulative frequency of preceding class

F: frequency of Median class

h= height of Median class

To find median class:

$\frac{n}{2} = \frac{600}{2} = 300$

search a class which has nearest to 300 in CF but not less than 300.

1000-2000 : Median class

l= 1000

n/2=300

cf=250

f=190

h= 1000

put these values to formula of median

$Median= 1000+ \bigg(\frac{ 300 - 250}{190} \bigg) \times 1000 \\ \\ Median = 1000 + \frac{50000}{190} \\ \\ = 1000 + 263.15 \\ \\Median = 1263.15$

Median income of families is 1263.15

Hope it helps you