Question

0
weekly income of 600 families is tabulated
Weekly income No. of famlies
o-looo
1000-2000
2000-3000
3000-4000
4ooo sooo
5000-6000
25
190
100
40
IS
S
Total 600
calculate the median income​

Answer 1

Answer:

Here We Go

solution:-

CI 0-1000 1000-2000 2000-3000 3000-4000 4000-5000 5000-6000

f.i 250 190 100 40 45 5

c.fi 250 440 540 580 595 600

N=600

Since,

2

N

=

2

600

=300

We know that ,

l=1000,i=1000,F=250,f=190

Median=l+

f

2

N

−F

×i

=1000+

190

2

600

−250

×1000

=1000+

190

50

×1000

=1000+

19

5000

=

19

19000+5000

=

19

24000

Hence,

Median=

19

24000

=1263.15

Answer 2

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