Question

Using a graph paper, draw an ogive for the following distribution which shows a record of the width 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:

1. The percentage of student weighting 55 kg or more
2. The weight above which the heaviest 30% of the student fall
3. The number of students who are
   1. underweight
   2. overweight, 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 students weighing more than 55 kg = 200 – 44 = 156 

Therefore, percentage of students weighing 55 kg or more 

= `156/200 xx 100`

= 78% 

ii. 30% of students = `(30 xx 200)/100 = 60` 

Heaviest 60 students in weight = 9 + 21 + 30 = 60 

Weight = 65 kg  ...(From table) 

iii. a. underweight students when 55.70 kg is standard = 46 (approx) from graph 

b. overweight student when 55.70 kg is standard = 200 – 46 = 154 (approx) from graph