Question

Compute the median for the following data:

Marks	No. of students
More than 150	0
More than 140	12
More than 130	27
More than 120	60
More than 110	105
More than 100	124
More than 90	141
More than 80	150

Answer 1

Marks	Class Internal	frequency (f.)	No. of students (c.f.)
More than 80	80-90	9	9
More than 90	90-100	17	26
More than 100	100-110	19	45
More than 110	110-120	45	90
More than 120	120-130	33	123
More than 130	130-140	15	138
More than 140	140-150	12	150
More than 150	150-160	0	150
		N = 150

We have, N = 150

∴ `"N"/2 = 150/2 = 75`

Thus, the cumulative frequency just greater than 75 is 90 and the corresponding class is 110-120.

Therefore, 110-120 is the median class.

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

∴ Median = `l + {(N/2-F)/f} × h`

∴ Median = `110 + {(75 - 45)/45} × 10`

∴ Median = `110 + (30)/45 × 10`

∴ Median = `110 + (300)/45`

∴ Median = 110 + 6.67

∴ Median = 116.67 (approx)

Hence, the median is 116.67.