The table below shows the distribution of the waiting times for some customers in a certain petrol station.
Waiting time (in mins)
No of customers
1.5 - 1.9
3
2.0 - 2.4
10
2.5 - 2.9
18
3.0 - 3.4
10
3.5 - 3.9
7
4.0 - 4.4
2
(a) Write down the class boundaries of the distribution.
(b) Construct a cumulative frequency curve for the data;
(c) Using your graph, estimate: (i) the interquartile range of the distribution ; (ii) the proportion of customers who could have waited for more than 3 minutes.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
Waiting time (in mins)
Class boundaries
No of customers
Cum Freq
1.5 - 1.9
1.45 - 1.95
3
3
2.0 - 2.4
1.95 - 2.45
10
13
2.5 - 2.9
2.45 - 2.95
18
31
3.0 - 3.4
2.95 - 3.45
10
41
3.5 - 3.9
3.45 - 3.95
7
48
4.0 - 4.4
3.95 - 4.45
2
50
(b)
(c) Interquartile range of the distribution = \(Q_{3} - Q_{1}\)
\(Q_{3} = \frac{3 \times 51}{4} = 38.25\)
\(Q_{1} = \frac{1 \times 51}{4} = 12.75\)
From the graph, \(Q_{3} = 3.25 ; Q_{1} = 2.45\)
\(\therefore \text{The interquartile range of the distribution } = 3.25 - 2.45 = 0.80\)
(ii) Proportion of customers who must have waited for more than 3 minutes = \(\frac{16}{50} = \frac{8}{25}\)
Source: Myschool Past Questions Archive (Record #54626)