Question

Find the mean and median of the following data:

Class	85 - 90	90 - 95	95 - 100	100 - 105	105 - 110	110 - 115
frequency	15	22	20	18	20	25

Answer 1

Class	Frequency	x	`bb(sumfx)`	c.f.
85 - 90	15	87.5	1312.5	15
90 - 95	22	92.5	2035.0	37
95 - 100	20	97.5	1950.0	57
100 - 105	18	102.5	1845.0	75
105 - 110	20	107.5	2150.0	95
110 - 115	25	112.5	2812.5	120
	`sum f_i` = 120		`sumf_i x_i` = 12105

∴ Mean = `(sumf_ix_i)/(sumf_i)`

= `12105/120`

= 100.875

Here,

`N/2` = `120/2` = 60

∴ 100 − 105 is the median class.

And

l = lower limit of median class = 100

h = Class interval = 90 − 85 = 5

c.f = Cumulative frequency of the class before median class = 57

f = frequency of the median class = 18

∴ Median = `l + (N/2 − c.f)/f xx h`

= `100 + (60 − 57)/18 xx 5`

= `100 + 3/18 xx 5`

= `100 + 5/6`

= 100 + 0.83

= 100.83