Question

Graph the following data in the form of 'less than' and 'more than' ogives; and calculate the median value through the graph:

Marks	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Number of Students	7	10	20	13	17	10	14	9

Answer 1

Estimation of the median

Less than and More than Ogive

Marks	Cumulative Frequency
Less than 5 Less than 10 Less than 15 Less than 20 Less than 25 Less than 30 Less than 35 Less than 40	7 7 + 10 = 17 17 + 20 = 37 37 + 13 = 50 50 + 17 = 67 67 + 10 = 77 77 + 14 = 91 91 + 9 = 100

Marks	Cumulative Frequency
More than 0 More than 5 More than 10 More than 15 More than 20 More than 25 More than 30 More than 35 More than 40	100 100 − 7 = 93 93 − 10 = 83 83 − 20 = 63 63 − 13 = 50 50 − 17 = 33 33 − 10 = 23 23 − 14 = 9 9 − 9 = 0

So, median is 20.