What is meant by ogive or cumulative frequency curve? From the following distribution construct the 'less than' ogive:

Capital (in lakh) 0−10 10−20 20−30 30−40 40−50 50−60 60−70

Number of Companies 2 3 7 11 15 7 23

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Solution

Ogives or cumulative frequency curve is a smooth distribution curve that depicts cumulative frequency data on a graph paper. For constructing a less than ogive, first the less than cumulative frequencies must be calculated as follows.

Capital
(in lakh) Cumulative Frequency

Less than 10
Less than 20
Less than 30
Less than 40
Less than 50
Less than 60
Less than 70 2
2 + 3 = 5
5 + 7 = 12
12 + 11 = 23
23 + 15 = 38
38 + 7 = 45
45 + 23 = 68

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.

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Profits (₹ in Lakhs)	10−20	20−30	30−40	40−50	50−60	60−70
No. of Companies	4	7	10	20	17	2

Age (in years)	10−20	20−30	30−40	40−50	50−60	60−70	70−80
No. of Persons	5	12	10	6	4	11	2

Marks Obtained	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Students	10	16	20	20	22	15	8	5

Age (yrs)	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Number of persons	5	15	20	23	17	11	9

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Capital (in lakh)	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Number of Companies	2	3	7	11	15	7	23

Capital (in lakh)	Cumulative Frequency
Less than 10 Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70	2 2 + 3 = 5 5 + 7 = 12 12 + 11 = 23 23 + 15 = 38 38 + 7 = 45 45 + 23 = 68