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AQA GCSE · Question 11.1 · Statistical Measures and Calculations
The table shows information about the heights of a sample of 100 trees in a forest. Complete the table below to show the cumulative frequencies for the data.
The table shows information about the heights of a sample of 100 trees in a forest. Complete the table below to show the cumulative frequencies for the data.
How to approach this question
Cumulative frequency is a "running total".
1. The first cumulative frequency is the same as the first frequency (8).
2. For the second row (h ≤ 10), add the frequency of that group (23) to the previous cumulative frequency (8). So, 8 + 23 = 31.
3. For the third row (h ≤ 15), add the frequency of that group (40) to the new cumulative frequency (31). So, 31 + 40 = 71.
4. Continue this process until you reach the last row. The final cumulative frequency should equal the total number of trees (100).
Full Answer
The completed cumulative frequency column should be: 8, 31, 71, 90, 100.
Cumulative frequency is the sum of the frequencies up to that point.
- For h ≤ 5: The frequency is 8. Cumulative frequency = 8.
- For h ≤ 10: The frequency is 23. Cumulative frequency = 8 + 23 = 31.
- For h ≤ 15: The frequency is 40. Cumulative frequency = 31 + 40 = 71.
- For h ≤ 20: The frequency is 19. Cumulative frequency = 71 + 19 = 90.
- For h ≤ 25: The frequency is 10. Cumulative frequency = 90 + 10 = 100.
The completed cumulative frequency column is: 8, 31, 71, 90, 100.
Common mistakes
✗ Just copying the frequencies across instead of calculating a running total.\n✗ Making an arithmetic error in the addition.
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