Question

Weekly income of 600 families is given below. Find the median.
Income 0-1000 1000-2000 2000-3000 3000-4000 4000-5000 5000-6000
fi 250 190 100 40 15 5

Answer 1

Answer :

We form our data table :

Class interval	Mid point ( x )	Frequency ( f )	fx	cumulative frequency cfb
0 - 1000	500	250	125000	250
1000 - 2000	1500	190	285000	250 + 190 = 440
2000 - 3000	2500	100	250000	440 + 100 = 540
3000 - 4000	3500	40	140000	540 + 40 = 580
4000 - 5000	4500	15	67500	580 + 15 = 595
5000 - 6000	5500	5	27500	595 + 5 = 600

${\sum }_{}$f = 600

${\sum }_{}$fx = 895000
So,

Mean = $\frac{{\sum }_{}fx}{{\sum }_{}f}=\frac{895000}{600}=\mathbf{1491}\mathbf{.}\mathbf{67}$
So,
Median group = 1000 - 2000
And
We know Median = $L+\frac{{\displaystyle \frac{n}{2}}-c{f}_b}{f_m}\times w$
Here

L = The lower class boundary of the group containing the median = 1000
n = The total number of data = 600
cf_b = The cumulative frequency of the groups before the median group = 250
f_m = The frequency of the median group = 190
w = The group width = 1000

So,

Median = $1000+\frac{{\displaystyle \frac{600}{2}-250}}{190}\times 1000=1000+\frac{{\displaystyle 300-250}}{190}\times 1000=1000+\frac{{\displaystyle 50\times 1000}}{190}=1000+\frac{{\displaystyle 50000}}{190}=1000+263.157=1263.157\approx \mathbf{1263}\mathbf{.}\mathbf{16}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathit{A}\mathit{n}\mathit{s}\mathbf{}\mathbf{)}\mathbf{}$