| Weight | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 | 75-80 |
| Frequency | 5 | 17 | 22 | 45 | 51 | 31 | 20 | 9 |
Use your ogive to estimate the following:
(i) The percentage of students weighing 55 kg or more.
(ii) The weight above which the heaviest 30% of the students fall,
(iii) The number of students who are :
- under-weight and
- over-weight, if 55.70 kg is considered as standard weight.
Solution:
We write the given data in cumulative frequency table.
| Weight | Frequency | Cumulative 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 |
To represent the data in the table graphically, we mark the upper limits of the class intervals on
the horizontal axis (x-axis) and their corresponding cumulative frequencies on the vertical axis ( y-axis),
Plot the points (45, 5), (50, 22), (55, 44), (60, 89), (65, 140), (70, 171), (75, 191) and (80, 200) on the graph.
Join the points with the free hand. We get an ogive as shown:
(i)Total number of students = 200
The number of students weighing 55 kg or more = 200-44 = 156 [From the graph]
Percentage = (156/200)×100
= 156/2
= 78%.
(ii)30% of 200 = (30/100)×200
= 30×2
= 60
No of heaviest students = 31+20+9 = 60
60 students fall above 65 kg.
(iii)If 55.70 kg is the standard weight,
No. of students who are under weight = 47 [from graph]
No. of students who are overweight = 200-47 = 153