Question

Find the median of the following frequency distribution:

Class:	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Frequency:	6	8	5	9	7

Answer 1

Class Interval	Frequency	Cumulative frequency (cf)
0 – 20	6	6
20 – 40	8	14
40 – 60	5	19
60 – 80	9	28
80 – 100	7	35
	N = `sumf_i` = 35

Here, N = 35

⇒ `"N"/2 = 35/2`

So, Median class is 40 – 60

Lower limit of median class (l) = 40

Class width (h) = 20

Frequency of median class (f) = 5

Precceding cf of median class (`"C"_f`) = 14

∴ Median = `l + ((N/2 - "C"_f)/f) xx h`

= `40 + ((35/2 - 14)/5) xx 20`

= 40 + 7 × 2

= 54