Using a graph paper, draw an ogive for the following distribution which shows a record of weight in kilograms of 100 students.
| Weight (in kg) | Number of students |
|---|---|
| 35–40 | 4 |
| 40–45 | 6 |
| 45–50 | 10 |
| 50–55 | 24 |
| 55–60 | 26 |
| 60–65 | 17 |
| 65–70 | 8 |
| 70–75 | 5 |
Use your ogive to estimate the following:
(a) the median weight of the students.
(b) percentage of students whose weight is 60 kg or more.
(c) the weight above which 20% of the students lie.
The cumulative-frequency table for the given continuous distribution is:
| Weight (in kg) | Number of students | Cumulative frequency |
|---|---|---|
| 35–40 | 4 | 4 |
| 40–45 | 6 | 10 |
| 45–50 | 10 | 20 |
| 50–55 | 24 | 44 |
| 55–60 | 26 | 70 |
| 60–65 | 17 | 87 |
| 65–70 | 8 | 95 |
| 70–75 | 5 | 100 |
(a) Total number of students, N = 100
Median position = \frac{\mathrm{N}}{2} = \frac{100}{2} = 50
From the ogive, the median weight is approximately 56 kg.
(b) Cumulative frequency at 60 kg = 70
Number of students weighing 60 kg or more = 100 − 70 = 30
Percentage = \frac{30}{100}\times100 = 30%
Therefore, 30% of the students weigh 60 kg or more.
(c) Number of students above the required weight = 20% of 100 = 20
Therefore, the cumulative frequency below the required weight = 100 − 20 = 80.
From the ogive, the weight corresponding to cumulative frequency 80 is approximately 63 kg.
Therefore, the weight above which 20% of the students lie is approximately 63 kg.
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