Question

A student draws a cumulative frequency curve for the marks obtained by 40 students of a class as shown below. Find the median marks obtained by the students of the class.

Answer 1

We know that, 

For finding median from a less than ogive or more than ogive curve, we follow below steps.

1. we find the sum of all frequencies or the last cumulative frequency in our given data, let that be N

2. Then we calculate \(\frac{N}{2}\)and locate the point corresponding to \(\frac{N}{2}\)th on the curve.

3. The X coordinate of the point located i.e. the class corresponding to \(\frac{N}{2}\)th cumulative frequency is the median of data. 

From the graph, we locate last cumulative frequency as 40 i.e. sum of all the frequencies is 40.

i.e. N = 40 and \(\frac{N}{2}\) = 20

Median is the marks corresponding to \(\frac{N}{2}\)th student.

In order to find the median, we first locate the point corresponding to 20^th student on Y axis. 

And from graph, that point is (50, 20) 

So, 

marks corresponding to 20^th student is 50. 

So, 

the median of above data is 50

So, 

the median of above data is 50