MathematicsExam code: 0580
Cumulative Frequency
Statistics
Running totals
- Cumulative frequency is a running total of the frequencies, so each entry counts everything up to and including that class
- It is used with grouped continuous data, where the individual values are not known
- Build the column by adding each class frequency to the total so far
- The final cumulative frequency must equal the total frequency, which is a built-in check on the arithmetic
- Each entry answers the question "how many are less than or equal to the end of this class"
| Time (t minutes) | Frequency | Cumulative frequency |
|---|---|---|
| 0 < t ⩽ 10 | 4 | 4 |
| 10 < t ⩽ 20 | 11 | 15 |
| 20 < t ⩽ 30 | 21 | 36 |
| 30 < t ⩽ 40 | 16 | 52 |
| 40 < t ⩽ 50 | 8 | 60 |
Worked example
Building a cumulative frequency table
The table shows the lengths of 40 fish. Work out the cumulative frequency for each class.
| Length (x cm) | Frequency |
|---|---|
| 20 < x ⩽ 30 | 4 |
| 30 < x ⩽ 40 | 9 |
| 40 < x ⩽ 50 | 14 |
| 50 < x ⩽ 60 | 8 |
| 60 < x ⩽ 70 | 5 |
Solution:
- Cumulative frequency is a running total, so each entry includes everything before it
- First class: 4
- Second: 4 + 9 = 13
- Third: 13 + 14 = 27
- Fourth: 27 + 8 = 35
- Fifth: 35 + 5 = 40
- The cumulative frequencies are 4, 13, 27, 35, 40
- The final entry must equal the total of all the frequencies, and 4 + 9 + 14 + 8 + 5 = 40 confirms it
- The values can only increase or stay the same; a column that falls anywhere has an arithmetic slip in it