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The cumulative frequency table shows information about the times, in minutes, taken by 40 people to complete a puzzle - Edexcel - GCSE Maths - Question 11 - 2019 - Paper 1
Question 11
The cumulative frequency table shows information about the times, in minutes, taken by 40 people to complete a puzzle. Time (m minutes) 20 < m ≤ 40 5 20 < m ≤ 60 ... show full transcript
Worked Solution & Example Answer:The cumulative frequency table shows information about the times, in minutes, taken by 40 people to complete a puzzle - Edexcel - GCSE Maths - Question 11 - 2019 - Paper 1
Step 1
On the grid below, draw a cumulative frequency graph for this information.
Answer
To construct the cumulative frequency graph, we will plot the cumulative frequency against the upper class boundaries of the corresponding time intervals. The points to plot are:
- (40, 5)
- (60, 25)
- (80, 38)
- (100, 40)
After plotting these points, connect them with a smooth curve, ensuring to label the graph accurately.
Step 2
Use your graph to find an estimate for the interquartile range.
Answer
To find the interquartile range, we need to determine the first quartile (Q1) and the third quartile (Q3) from the graph. From the cumulative frequency of 40, calculate:
- Q1: Locate the point at the 10th percentile (0.25 * 40 = 10) on the vertical axis and trace horizontally to find the corresponding time on the horizontal axis.
- Q3: Locate the point at the 30th percentile (0.75 * 40 = 30) and do the same. The interquartile range is given by Q3 - Q1.
Step 3
Use your graph to find an estimate for the probability that this person took between 50 minutes and 90 minutes to complete the puzzle.
Answer
To calculate this probability from the graph, first determine the cumulative frequencies at 50 minutes and 90 minutes by tracing up from these time values to the graph- follow horizontally and back down to read the frequencies. The probability is then calculated as:
where C(90) and C(50) are the cumulative frequencies corresponding to 90 and 50 minutes, respectively.