Question

Using a graph paper, drawn an Ogive for the following distribution which shows a record of the weight in kilograms of 200 students.

Weight	Frequency
40 - 45	5
45 - 50	17
50 - 55	22
55 - 60	45
60 - 65	51
65 - 70	31
70 - 75	20
75 - 80	9

Use your ogive to estimate the following:
(i) The percentage of students weighing 55kg or more.
(ii) The weight above which the heaviest 30% of the students fall.
(iii) The number of students who are:
(1) under-weight and
(2) over-weight, if 55·70 kg is considered as standard weight.

Answer 1

Weight	Frequency	c.f.
40 - 45	5	5
45 - 50	17	22
50 - 55	22	44
55 - 60	45	89
60 - 65	51	140
65 - 70	31	171
70 - 75	20	191
75 - 80	9	200

(i) Number of student weighing 55 kg or more
= 200 - 44
= 156
∴ Percentage = `(156 xx 100)/(200)`
= 78%.

(ii) 30% of 200 = 60
∴  Heaviest w.t. (least) 
= w.t. of 200 - 60
= 140th student
= 65 kg or more.
(iii) From ogive c.f. against 55.70 kg
= 45
∴  (1) number of under w.t. students
= 44
(2) number of over w.t. students
= 200 - 44
= 156.