The annual rainfall record of a city for 66 days is given in the following table:

Rainfall (in cm):	0-10	10-20	20-30	30-40	40-50	50-60
Number of days:	22	10	8	15	5	6

Calculate the median rainfall using ogives of more than type and less than type.

Given:

To do:

We have to calculate the median rainfall using ogives of more than type and less than type.

Solution:

We first prepare the cumulative  frequency distribution table by less than method as given below:

Represent upper class limits along X-axis and cumulative frequency along Y-axis.

Plot the points (0,0), (10,22), (20,32), (30, 40), (40, 55), (50, 60) and (60, 66) on the graph and join them in free hand to get a less than ogive.

We first prepare the cumulative  frequency distribution table by more than method as given below:

Represent lower class limits along X-axis and cumulative frequency along Y-axis.

Plot the points (0, 66), (10, 44), (20, 34), (30, 26), (40, 11) and (50, 6) on the graph and join them in a free hand to get a more than ogive.

Total number of days $N = 66$

This implies,

$\frac{N}{2} = \frac{66}{2}=33$

Draw a line parallel to X-axis at the point of intersection of both ogives, which further intersect at (0, 33) on Y-axis.

Draw a line perpendicular to X-axis at point of intersection of both ogives, which further intersect at (21.25, 0) on X-axis.

Therefore, 21.25 is the required median using ogives.

Hence, the median rainfall is 21.25 cm.

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Updated on: 10-Oct-2022

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