Question

The table given below shows the amount of sales of 100 companies:

Sales (₹ in crores)	20−30	30−40	40−50	50−60	60−70	70−80
No. of Companies	7	12	15	30	22	14

With the help of information given above, prepare: (i) 'Less than' ogive; (ii) 'More than" ogive; and (iii) 'Less than' ogive.

Answer 1

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

Sales	No. of Companies
Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80	7 19 34 64 86 100

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.



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

Sales	No. of companies
More than 20 More than 30 More than 40 More than 50 More than 60 More than 70	100 100 − 7 = 93 93 − 12 = 81 81 − 15 = 66 66 − 30 = 36 36 − 22 = 14

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.




(iii) 'Less than' and 'More than' ogive