Question

Draw 'less than' and 'more than' ogive curves from the following data:

Marks	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Number of Students	7	10	20	13	12	19	14	9

Answer 1

(i) For constructing a less than ogive, first the given frequency distribution must be converted into a less than cumulative frequency distribution as follows.

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 + 12 = 62 62 + 19 = 81 81 + 14 = 95 95 + 9 = 104

We now plot the cumulative frequencies against the upper limit of the class intervals. The curve obtained on joining the points so plotted is known as the less than ogive.



(ii) For constructing a less than ogive, first the given frequency distribution is converted into a more than cumulative frequency distribution as follows. ​

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	104 104 − 7 = 97 97 − 10 = 87 87 − 20 = 67 67 − 13 = 54 54 − 12 = 42 42 − 19 = 23 23 − 14 = 9 9 − 9 = 0

We now plot the cumulative frequencies against the lower limit of the class intervals. The curve obtained on joining the points so plotted is known as the more than ogive.