Question

Find the median for the given frequency distribution:

Class	Frequency
40 – 50	2
45 – 50	3
50 – 55	8
55 – 60	6
60 – 65	6
65 – 70	3
70 – 75	2

Answer 1

Class	Frequency	c.f.
40 – 45	2	2
45 – 50	3	5
50 – 55	8	13
55 – 60	6	19
60 – 65	6	25
65 – 70	3	28
70 – 75	2	30
	N = 30

Median = `"N"/2`

= `30/2`

= 15

The cumulative frequency just greater than 15 is 19 and the corresponding class is 55 – 60.

So, Median class = 55 – 60

l = 55, f = 6, c.f. = 13 and h = 5

Median = `l + ((N/2 - c.f.))/f xx h`

= `55 + ((15 - 13)/6) xx 5`

= `55 + 5/3`

= 55 + 1.67

= 56.67   ...(Approx)