Cumulative relative frequency tells you, step by step, what fraction (or percentage) of all data values are less than or equal to a given value.

Quick Scoop

Think of a list of data values sorted from smallest to largest. At each value, you can ask: “What proportion of all observations are at this value or below it?” That running proportion is the cumulative relative frequency.

Key ideas

  • Frequency : How many times a value occurs.
  • Relative frequency : Frequency ÷ total number of observations (a fraction or percentage of the whole).
  • Cumulative frequency : Running total of frequencies up to and including a value.
  • Cumulative relative frequency : Running total of relative frequencies up to and including a value.

So, at each row of a frequency table, you add the new relative frequency to all previous ones. By the last row, the cumulative relative frequency will always be 1 (or 100%).

Simple example story

Imagine you test how many hours 10 students studied:

  • 1 hour: 2 students
  • 2 hours: 3 students
  • 3 hours: 5 students

Total students = 10. Relative frequencies:

  • 1 hour: 2/10 = 0.2 (20%)
  • 2 hours: 3/10 = 0.3 (30%)
  • 3 hours: 5/10 = 0.5 (50%)

Cumulative relative frequencies:

  • Up to 1 hour: 0.2
  • Up to 2 hours: 0.2 + 0.3 = 0.5
  • Up to 3 hours: 0.5 + 0.5 = 1.0 (100%)

This tells you, for example, that 50% of students studied 2 hours or less, and 100% studied 3 hours or less.

Why it matters now

Cumulative relative frequency is widely used in statistics to understand distributions, build graphs like ogives, and answer “how many at or below this point?” types of questions in data analysis, surveys, and dashboards.

In short: cumulative relative frequency is the running total of proportions or percentages up to each data value, ending at 1 (or 100%).

Information gathered from public forums or data available on the internet and portrayed here.