What is Cumulative Relative Frequency?
Cumulative relative frequency is the running total of relative frequencies up to a certain point in an ordered dataset. It tells you the proportion of values that fall at or below a specific category or data value, making it useful for understanding how data accumulate across intervals.
To calculate cumulative relative frequency:
- Start with a frequency table that includes the count for each category or interval.
- Calculate the relative frequency for each group by dividing each count by the total number of observations.
- Add each relative frequency to the sum of all previous ones to get the cumulative value.
The values range from 0 to 1, and the final entry in the table should always equal 1 (or 100% if expressed as a percentage). These frequencies are especially helpful for identifying percentiles and medians, or for plotting ogive graphs.
Example Calculations
For example, a teacher records the number of quiz scores falling into different score ranges for a class of 40 students. The table below shows the frequency table, relative frequency, and cumulative relative frequency for each score range:
| Score Range | Frequency | Relative Frequency | Cumulative Relative Frequency |
| 0–60 | 4 | 0.10 | 0.10 |
| 61–70 | 6 | 0.15 | 0.25 |
| 71–80 | 8 | 0.20 | 0.45 |
| 81–90 | 12 | 0.30 | 0.75 |
| 91–100 | 10 | 0.25 | 1.00 |
This table helps answer questions like: What proportion of students scored 80 or less? How many scored 90 or below?
- For scores of 80 or below (combining the ranges 0–60, 61–70, and 71–80), 18 students fall into these categories. That gives a cumulative relative frequency of 18 ÷ 40 = 0.45, meaning 45% of students scored 80 or lower.
- At 90 or below, the total increases to 30 students, giving a cumulative percentage of 30 ÷ 40 = 0.75, or 75% of students scored 90 or lower.
- The final point on the graph, 100, corresponds to a cumulative proportion of 1.0, confirming that 100% of students scored 100 or below.
The graph below corresponds to the cumulative relative frequencies in the table and makes it easy to see how scores accumulate and helps identify percentiles and medians visually.
