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Feb/Mar 2016 p62 q4
2394
A survey was made of the journey times of 63 people who cycle to work in a certain town. The results are summarised in the following cumulative frequency table.
Journey time (minutes)
≤ 10
≤ 25
≤ 45
≤ 60
≤ 80
Cumulative frequency
0
18
50
59
63
State how many journey times were between 25 and 45 minutes.
Draw a histogram on graph paper to represent the data.
Calculate an estimate of the mean journey time.
Solution
(i) To find the number of journey times between 25 and 45 minutes, subtract the cumulative frequency at 25 minutes from the cumulative frequency at 45 minutes: \(50 - 18 = 32\).
(ii) To draw the histogram, calculate the frequency for each interval: \([0, 10]: 0\), \((10, 25]: 18\), \((25, 45]: 32\), \((45, 60]: 9\), \((60, 80]: 4\). Then, calculate the frequency density by dividing the frequency by the class width: \(\frac{18}{15} = 1.2\), \(\frac{32}{20} = 1.6\), \(\frac{9}{15} = 0.6\), \(\frac{4}{20} = 0.2\). Draw bars with these heights.
(iii) To estimate the mean journey time, use the midpoints of each interval: \((17.5 \times 18) + (35 \times 32) + (52.5 \times 9) + (70 \times 4)\). Sum these products and divide by the total frequency: \(\frac{2187.5}{63} = 34.7\) minutes.
