Question

Draw a 'Less than' and 'More than' ogive from the following distribution:

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

Answer 1

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

Less than	No. of Companies
Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70	4 4 + 7 = 11 11 + 10 = 21 21 + 20 = 41 41 + 17 = 58 58 + 2 = 60

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



For constructing more than ogive, first the given frequency distribution must be converted into more than cumulative frequency distribution as follows.

More than	No. of companies
More than 10 More than 20 More than 30 More than 40 More than 50 More than 60	60 60 − 4 = 56 56 − 7 = 49 49 − 10 = 39 39 − 20 = 19 19 − 17 = 2

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