Question

Calculate the median of marks of students for the following distribution:

Marks	Number of students
More than or equal to 0	100
More than or equal to 10	93
More than or equal to 20	88
More than or equal to 30	70
More than or equal to 40	59
More than or equal to 50	42
More than or equal to 60	34
More than or equal to 70	20
More than or equal to 80	11
More than or equal to 90	4

Answer 1

Marks Students	Number of Interval	Class `(f_i)`	Frequency frequency `(c.f.)`	Cumulative
More than or equal to 0	100	0 – 10	100 – 93 = 7	7
More than or equal to 10	93	10 –20	93 – 88 = 5	12
More than or equal to 20	88	20 –30	88 – 70 = 18	30
More than or equal to 30	70	30 –40	70 – 59 = 11	41
More than or equal to 40	59	40 –50	59 – 42 = 17	58
More than or equal to 50	42	50 – 60	42 –34 = 8	66
More than or equal to 60	34	60 – 70	34 – 20 = 14	80
More than or equal to 70	20	70 –80	20 –11 = 9	89
More than or equal to 80	11	80 – 90	11 – 4 = 7	96
More than or equal to 90	4	90 – 100	4 – 0 = 4	100
			`sumf_i` = 100

From the table, N = 100

∴ `N/2 = 100/2` = 50

Cumulative frequency (c.f.) just greater than 50 is 58, belonging to interval 40 – 50.

∴ Median class = 40 – 50

So, L = 40, f = 17, c.f. = 41, h = 10

Now, Median = `L + ((N/2 - c.f.)/f) xx h`

= `40 + ((50 - 41)/17) xx 10`

= `40 + (9/17) xx 10`

= 40 + 5.294

= 45.294

As a result, the median score is 45.294.