Question

Find the median of the following data by making a 'less than ogive'. [CBSE 2014]

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80	80−90	90−100
Number of students	5	3	4	3	3	4	7	9	7	8

Answer 1

The frequency distribution table of less than type is given as follows:

Marks (upper class limits)	Cumulative frequency (cf)
Less than 10	5
Less than 20	5 + 3 = 8
Less than 30	8 + 4 = 12
Less than 40	12 + 3 = 15
Less than 50	15 + 3 = 18
Less than 60	18 + 4 = 22
Less than 70	22 + 7 = 29
Less than 80	29 + 9 = 38
Less than 90	38 + 7 = 45
Less than 100	45 + 8 = 53

Taking upper class limits of class intervals on x−axis and their respective frequencies on y−axis, its ogive can be drawn as follows:



Here, N = 53 $\Rightarrow \frac{N}{2}=26.5$.

Mark the point A whose ordinate is 26.5 and its x−coordinate is 66.4.



Thus, median of the data is 66.4.