Question

The production yield per hectare of wheat of some farms of a village are given in the following table:

Production yield (in kg/ha)	40−45	45−50	50−55	55−60	60−65	65−70	70−75	75−80	80−85
Number of farms	1	9	15	18	40	26	16	14	10

Draw a less than type ogive and a more than type ogive for this data.

Answer 1

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

Production yield (in kg/ha) (upper class limits)	Cumulative frequency (cf)
Less than 45	1
Less than 50	1 + 9 = 10
Less than 55	10 + 15 = 25
Less than 60	25 + 18 = 43
Less than 65	43 + 40 = 83
Less than 70	83 + 26 = 109
Less than 75	109 + 16 = 125
Less than 80	125 + 14 = 139
Less than 85	139 + 10 = 149

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

​

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

Production yield (in kg/ha) (lower class limits)	Cumulative frequency (cf)
More than 40	148 + 1 = 149
More than 45	139 + 9 = 148
More than 50	124 + 15 = 139
More than 55	106 + 18 = 124
More than 60	66 + 40 = 106
More than 65	40 + 26 = 66
More than 70	24 + 16 = 40
More than 75	10 + 14 = 24
More than 80	10

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