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.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(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(\(\geq 60kg = \frac{25}{100} = \frac{1}{4}\)
Source: Myschool Past Questions Archive (Record #52836)