Calculate the median from the following data:

Marks

0 – 10

10 – 30

30 – 60

60 – 80

80 – 90

Number of students

5

15

30

8

2

Answer:

First, prepare the cumulative frequency table:

Marks

Number of students

Cumulative frequency

0 – 10

5

5

10 – 30

15

5 + 15 = 20

30 – 60

30

20 + 30 = 50

60 – 80

8

50 + 8 = 58

80 – 90

2

58 + 2 = 60

Here N = 60

∴ n = 60/2 = 30

The cumulative frequency (c.f) just greater than 30 is 50.

The corresponding class (Median class) = 30 – 60

l = 30

c.f = 30

F= 20

h = 30

\(Median = l + \frac{\frac{N}{2} – F}{c.f}\times h\) \(Median = 30 + \frac{ 30 – 20}{30}\times 30\)

Median = 40

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