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Statistical Measures and CalculationsFoundationcumulative frequencytables

AQA GCSE · Question 11.1 · Statistical Measures and Calculations

Height, h (m)Frequency0 < h ≤ 585 < h ≤ 102310 < h ≤ 154015 < h ≤ 201920 < h ≤ 2510Height, h (m)FrequencyCumulative frequency0 < h ≤ 5885 < h ≤ 102310 < h ≤ 154015 < h ≤ 201920 < h ≤ 2510

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

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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