What Is Relative Cumulative Frequency?
Relative cumulative frequency is the share of all observations that fall at or below a given value. You get it by dividing each running total of frequencies by the total number of observations.
Enter your data and the calculator groups it, adds the running totals and converts them to proportions and percentages. The last row always reaches 1, or 100 percent.
Use the table to read percentiles and the median, or draw the ogive to see how the data accumulates.
How to Use the Relative Cumulative Frequency Calculator
- Choose values and frequencies, or paste raw data.
- Read the table row by row.
- Use the ogive to estimate medians and percentiles.
Relative Cumulative Frequency Formula
Relative frequency
Cumulative frequency
Relative cumulative frequency
Relative Cumulative Frequency Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| f | Frequency, how many times a value or class occurs | |
| n | Total number of observations | Sum of all f |
| Cumulative f | Running total of frequencies | |
| Relative cumulative f | Cumulative f divided by n | Ends at 1 |
Relative Cumulative Frequency Worked Example
With the example values loaded in the calculator above, the steps are:
- Relative frequency = frequency ÷ N, where N is the total frequency.
- N = 40.
- Cumulative frequency adds the frequencies running down the table.
- Relative cumulative frequency = cumulative frequency ÷ N, so the last row is 1.
- The running share first reaches 50% at x = 3.
Result: Total frequency N = 40; Final relative cumulative frequency = 1 (100%).
Worked example
Values 1 to 6 with frequencies 4, 7, 12, 9, 5, 3 give N = 40. The cumulative frequencies are 4, 11, 23, 32, 37, 40.
Dividing by 40 gives relative cumulative frequencies of 0.10, 0.275, 0.575, 0.80, 0.925 and 1. The share first passes 50% at the value 3, so the median is 3.
What you can read from it
A relative cumulative frequency of 0.575 at x = 3 means 57.5% of the observations are 3 or less. Reading across at 0.25, 0.50 and 0.75 gives estimates of the quartiles.
Where Relative Cumulative Frequency Is Used
Finding percentiles
Read the value below which a given share of the data falls.
Drawing an ogive
Plot cumulative percentages against class boundaries.
Statistics coursework
Complete frequency tables with relative and cumulative columns.
Common Relative Cumulative Frequency Mistakes to Avoid
- The last relative cumulative frequency must be exactly 1.
- For class intervals, accumulate up to the upper class boundary.
Relative Cumulative Frequency Terms and Definitions
- Ogive
- A graph of cumulative frequency against the upper class boundaries.
Relative Cumulative Frequency FAQs
What is relative cumulative frequency?
The proportion of the data at or below a given value, found by dividing cumulative frequency by the total.
How do you calculate it?
Divide each frequency by N, then add the results running down the table, or divide the cumulative frequency by N.
What is the difference between relative and cumulative frequency?
Relative frequency is a share of the total for one value. Cumulative frequency is a running total.
What should the last value be?
Exactly 1, or 100%.
How do I find the median from it?
Find the first value where the relative cumulative frequency reaches 0.5.
Can I use raw data?
Yes. The calculator counts each distinct value for you.