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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) ... 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 draw the cumulative frequency graph, plot the cumulative frequencies against the upper boundary of each time interval:
- For the interval 20 < m ≤ 40, plot the point (40, 5).
- For the interval 20 < m ≤ 60, plot the point (60, 25).
- For the interval 20 < m ≤ 80, plot the point (80, 38).
- For the interval 20 < m ≤ 100, plot the point (100, 40).
Draw a smooth curve passing through these points. Make sure the graph is labeled appropriately and includes a title.
Step 2
Use your graph to find an estimate for the interquartile range.
Answer
To find the interquartile range, first determine the first quartile (Q1) and third quartile (Q3) from the graph:
- Q1 is the value where 25% of the data lies, which corresponds to a cumulative frequency of 10 (since 25% of 40 is 10). Locate this on the graph and find the corresponding time value.
- Q3 is the value where 75% of the data lies, corresponding to a cumulative frequency of 30. Locate this on the graph and find the corresponding time value.
Then, calculate the interquartile range (IQR) using the formula:
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 estimate the probability, first determine the cumulative frequencies for 50 minutes and 90 minutes from the graph:
- Identify the cumulative frequency at 50 minutes and subtract it from the cumulative frequency at 90 minutes to find the number of people who took between these times.
- Then, divide this number by the total number of people (40) to find the probability: