Question

The table given below shows the weekly expenditures on food of some households in a locality

Weekly expenditure (in Rs)	Number of house holds
100 – 200	5
200- 300	6
300 – 400	11
400 – 500	13
500 – 600	5
600 – 700	4
700 – 800	3
800 – 900	2

Draw a ‘less than type ogive’ and a ‘more than type ogive’ for this distribution.

Answer 1

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

Weekly expenditure (in Rs) (upper class limits)	Cumulative frequency (cf)
Less than 200	5
Less than 300	5 + 6 = 11
Less than 400	11 + 11 = 22
Less than 500	22 + 13 = 35
Less than 600	35 + 5 = 40
Less than 700	40 + 4 = 44
Less than 800	44 + 3 = 47
Less than 900	47 + 2 = 49

Taking the lower class limits on x-axis and their respective cumulative frequencies on y-axis, its ogive can be obtained as follows

Now,
The frequency distribution table of more than type is as follows:

Weekly expenditure (in Rs) (lower class limits)	Cumulative frequency (cf)
More than 100	44 + 5 = 49
More than 200	38 + 6 = 44
More than 300	27 + 11 = 38
More than 400	14 + 13 = 27
More than 500	9 + 5 = 14
More than 600	5 + 4 = 9
More than 700	2 + 3 = 5
More than 800	2

Taking the lower class limits
on x-axis and their respective
cumulative frequencies on y-axis,
its ogive can be obtained as follows: