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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 will add the frequencies cumulatively:
- For the interval 0 < t ≤ 20, the cumulative frequency is 5.
- For 20 < t ≤ 40, we add 10 (5 + 10 = 15).
- For 40 < t ≤ 60, we add 20 (15 + 20 = 35).
- For 60 < t ≤ 80, we add 15 (35 + 15 = 50).
- For 80 < t ≤ 100, we add 8 (50 + 8 = 58).
- For 100 < t ≤ 120, we add 2 (58 + 2 = 60).
Thus, the completed cumulative frequency table is:
| Time (t minutes) | Cumulative frequency |
|---|---|
| 0 < t ≤ 20 | 5 |
| 20 < t ≤ 40 | 15 |
| 40 < t ≤ 60 | 35 |
| 60 < t ≤ 80 | 50 |
| 80 < t ≤ 100 | 58 |
| 100 < t ≤ 120 | 60. |
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 upper boundaries of each interval on the graph provided. Use the following points:
- (20, 5)
- (40, 15)
- (60, 35)
- (80, 50)
- (100, 58)
- (120, 60)
Once all points have been plotted, connect the points with a smooth curve or straight lines to create the cumulative frequency graph.
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
From the graph, locate the cumulative frequency at 90 minutes:
-
Find the point on the graph where t = 90 and read the cumulative frequency value. For example, if the value is estimated at 70, this means 70 workers take 90 minutes or less.
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To find the number of workers who take more than 90 minutes, subtract this value from the total number of workers: 80 - 70 = 10.
-
Finally, to find the percentage: (10 / 80) * 100 = 12.5%.
Thus, approximately 12.5% of the office workers take more than 90 minutes to get to work.