# 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

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