Compute the median for each of the following data (i) Marks No. of students (ii) Marks No. of students Less than 10 0 More than150 0 Less than 30 10 More than140 12 Less than 50 25 More than130 27 Less than 70 43 More than120 60 Less than 90 65 More than110 105 Less than 110 87 More than100 124 Less than 130 96 More than90 141 Less than 150 100 More than80 150

Question

Philoid · Accepted Answer

(i)

Marks	No. of students	Class interval	Frequency	Cumulative frequency
Less than 10	0	0-10	0	0
Less than 30	10	10-30	10	10
Less than 50	25	30-50	15	25
Less than 70	43	50-70	18	43 (F)
Less than 90	65	70-90	22 (f)	65
Less than 110	87	90-110	22	87
Less than 130	96	110-130	9	96
Less than 150	100	130-150	4	100
			N = 100

We have, N = 100

= = 50

The cumulative frequency just greater than is 65 then median Class 70-90, such that:

l = 70, f = 22, F = 43, h = 20

Median = l + * h

= 70 + * 20

= 70 +

= 70 + 6.36 = 76.36

(ii)

Marks	No. of students	Class interval	Frequency	Cumulative frequency
More than 80f	150	80-90	9	9
More than 90	141	90-100	17	16
More than 100	124	100-110	19	45 (F)
More than 110	105	110-120	45 (f)	90
More than 120	60	120-130	33	123
More than 130	27	130-140	15	138
More than 140	12	140-150	12	150
More than 150	0	150-160	0	150
			N = 150

We have, N = 150

= = 7

The cumulative frequency is just more than is 90 then, the Median Class is 110-120 such that:

l = 110, f = 45, F = 45, h = 10

Median = l + * h

= 110 + * 10

= 110 +

= 110 + 6.67

= 116.67

(i) Marks	No. of students	(ii) Marks	No. of students
Less than 10	0	More than150	0
Less than 30	10	More than140	12
Less than 50	25	More than130	27
Less than 70	43	More than120	60
Less than 90	65	More than110	105
Less than 110	87	More than100	124
Less than 130	96	More than90	141
Less than 150	100	More than80	150