Question

Find the median for the following frequency distribution table:Class-interval 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 Frequency 5 3 9 10 8 5

Answer 1

Solution:

Sum of frequencies

$5 + 3 + 9 + 10 + 8 + 5 \\ \\ = 40$
So,

$\frac{n}{2} = 20$
Class-interval Frequency CF
0 - 5 _________5______5

5 - 10_________3______8

10 - 15_________9______17

15 - 20________10______27

20 - 25 ________8_______35

25 - 30 _________5_______40

so just upper nearby class of n/2 is 15-20

So, 15-20 is median class

l= 15

cf= 17

f =10

h = 5

put all these values in the formula


$Median= l + ( \frac{ \frac{n}{2} - cf }{f} )h \\ \\ = 15 + ( \frac{20 - 17}{10})5 \\ \\ = 15 + \frac{3}{2} \\ \\ = 15 + 1.5 \\ \\ = 16.5$
Median = 16.5

Hope it helps you.