Use graph paper to answer this question.
During a medical check-up of 60 students in a school, their weights were recorded as follows:
| Weight (kg) | Number of students |
|---|---|
| 28–30 | 2 |
| 30–32 | 4 |
| 32–34 | 10 |
| 34–36 | 13 |
| 36–38 | 15 |
| 38–40 | 9 |
| 40–42 | 5 |
| 42–44 | 2 |
Taking 2 cm = 2 kg along one axis and 2 cm = 10 students along the other axis, draw an ogive. Use the graph to find:
(a) the median
(b) the upper quartile
(c) the number of students whose weight is above 37 kg.
First calculate the less-than cumulative frequencies:
| Weight (kg) | f | Cumulative frequency |
|---|---|---|
| 28–30 | 2 | 2 |
| 30–32 | 4 | 6 |
| 32–34 | 10 | 16 |
| 34–36 | 13 | 29 |
| 36–38 | 15 | 44 |
| 38–40 | 9 | 53 |
| 40–42 | 5 | 58 |
| 42–44 | 2 | 60 |
Plot (28, 0), (30, 2), (32, 6), (34, 16), (36, 29), (38, 44), (40, 53), (42, 58) and (44, 60), then join them with a smooth curve.
(a) Total students, n = 60.
⇒ Median position = \frac{60}{2} = 30th observation.
From the ogive, the median ≈ 36.2 kg.
(b) Upper-quartile position = \frac{3×60}{4} = 45th observation.
From the ogive, Q₃ ≈ 38.2 kg.
(c) From the ogive, approximately 38 students weigh 37 kg or less.
⇒ Number above 37 kg = 60 − 38
⇒ Number above 37 kg = 22
Therefore: median ≈ 36.2 kg, upper quartile ≈ 38.2 kg, and 22 students weigh above 37 kg.
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