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

1. Less than type cumulative frequency table

For a less than ogive, we plot the upper class limits on the x-axis and their corresponding less than cumulative frequencies on the y-axis.

Production yield (Upper Limit)	Number of farms (Frequency)	Less than Cumulative Frequency (cf)	Plotting points (x, y)
Less than 45	1	1	(45, 1)
Less than 50	9	1 + 9 = 10	(50, 10)
Less than 55	15	10 + 15 = 25	(55, 25)
Less than 60	18	25 + 18 = 43	(60, 43)
Less than 65	40	43 + 40 = 83	(65, 83)
Less than 70	26	83 + 26 = 109	(70, 109)
Less than 75	16	109 + 16 = 125	(75, 125)
Less than 80	14	125 + 14 = 139	(80, 139)
Less than 85	10	139 + 10 = 149	(85, 149)

2. More than type cumulative frequency table

For a more than ogive, we plot the lower class limits on the x-axis and their corresponding more than cumulative frequencies on the y-axis.

Production yield (Lower Limit)	Number of farms (Frequency)	More than Cumulative Frequency (cf)	Plotting Points (x, y)
More than or equal to 40	1	149	(40, 149)
More than or equal to 45	9	149 – 1 = 148	(45, 148)
More than or equal to 50	15	148 – 9 = 139	(50, 139)
More than or equal to 55	18	139 – 15 = 124	(55, 124)
More than or equal to 60	40	124 – 18 = 106	(60, 106)
More than or equal to 65	26	106 – 40 = 66	(65, 66)
More than or equal to 70	16	66 – 26 = 40	(70, 40)
More than or equal to 75	14	40 – 16 = 24	(75, 24)
More than or equal to 80	10	24 – 14 = 10	(80, 10)
More than or equal to 85	-	0	(85, 0)

3. Ogive Graph

Below is the visual representation of both the Less Than and More Than type ogives plotted on the same axes. The point where both curves intersect gives the median of the data.