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The grouped frequency table gives information about the times, in minutes, that 80 office workers take to get to work - Edexcel - GCSE Maths - Question 12 - 2019 - Paper 2
Question 12
The grouped frequency table gives information about the times, in minutes, that 80 office workers take to get to work. (a) Complete the cumulative frequency table: ... show full transcript
Worked Solution & Example Answer:The grouped frequency table gives information about the times, in minutes, that 80 office workers take to get to work - Edexcel - GCSE Maths - Question 12 - 2019 - Paper 2
Step 1
Complete the cumulative frequency table:
Answer
To complete the cumulative frequency table, we need to add the frequencies cumulatively for each time interval:
- For the interval 0 < t ≤ 20, the cumulative frequency is 5.
- For the interval 20 < t ≤ 40, the cumulative frequency is 5 + 30 = 35.
- For the interval 40 < t ≤ 60, the cumulative frequency is 35 + 20 = 55.
- For the interval 60 < t ≤ 80, the cumulative frequency is 55 + 15 = 70.
- For the interval 80 < t ≤ 100, the cumulative frequency is 70 + 8 = 78.
- For the interval 100 < t ≤ 120, the cumulative frequency is 78 + 2 = 80.
Thus, the completed table will look as follows:
Time (t minutes) Cumulative frequency 0 ≤ t < 20 5 0 ≤ t < 40 35 0 ≤ t < 60 55 0 ≤ t < 80 70 0 ≤ t < 100 78 0 ≤ t < 120 80
Step 2
On the grid, draw the cumulative frequency graph for this information:
Answer
To draw the cumulative frequency graph, plot the cumulative frequencies against the time intervals on the grid:
- The points to plot are (20, 5), (40, 35), (60, 55), (80, 70), (100, 78), and (120, 80).
Connect these points with a smooth curve or straight lines, making sure each segment is consistent.
Step 3
Use your graph to find an estimate for the percentage of these office workers who take more than 90 minutes to get to work:
Answer
To estimate the percentage of office workers taking more than 90 minutes:
-
Identify the cumulative frequency at 90 minutes from the graph, which appears to be about 80.
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The cumulative frequency for 120 minutes (all workers) is 80.
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So, the number of workers taking more than 90 minutes is given by:
[ 80 - 78 = 2 ]
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Therefore, the percentage of these workers is:
[ \frac{2}{80} \times 100% = 2.5% ]
Thus, approximately 2.5% of the office workers take more than 90 minutes to get to work.