The frequency distribution of the weight of 100 participants in a high jump competition is as shown below :
| Weight (kg) | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 | 60 – 69 | 70 – 79 |
|
Number of Participants |
10 | 18 | 22 | 25 | 16 | 9 |
(a) Construct the cumulative frequency table.
(b) Draw the cumulative frequency curve.
(c) From the curve, estimate the : (i) median ; (ii) semi- interquartile range ; (iii) probability that a participant chosen at random weighs at least 60 kg.
Explanation
(a)
|
Class Intervals |
freq |
cum freq |
class boundaries |
| 20 - 29 | 10 | 10 | 19.5 - 29.5 |
| 30 - 39 | 18 | 28 | 29.5 - 39.5 |
| 40 - 49 | 22 | 50 | 39.5 - 49.5 |
| 50 - 59 | 25 | 75 | 49.5 - 59.5 |
| 60 - 69 | 16 | 91 | 59.5 - 69.5 |
| 70 - 79 | 9 | 100 | 69.5 - 79.5 |
(b) 
(c) (i) Median (\(Q_{2}\)) = 49.5
(ii) Semi- Interquartile range = \(\frac{1}{2} (Q_{3} - Q_{1})\)
\(Q_{1} = 38.5\); \(Q_{3} = 59.5\).
Semi- Interquartile range = \(\frac{1}{2} (59.5 - 38.5)\)
= \(\frac{1}{2} (21)\)
= 10.5.
(iii) Pr(\(\geq 60kg = \frac{25}{100} = \frac{1}{4}\)