Cumulative Frequency

What Is Cumulative Frequency?

Cumulative frequency is one of the most useful tools in statistics because it helps you understand the full picture of grouped data. Let's break it down.

The Core Idea: Running Total

Cumulative literally means "adding up as you go along" — like a running total. In a table of grouped data, cumulative frequency means you total up all the frequencies from the start up to the end of each class interval.

Think of it like this: if you're counting students in a class by height, and you want to know "how many students are 150 cm tall or less", you'd add up all the frequencies for every height group up to and including 150 cm. That's cumulative.

Two Ways Tables Are Presented

Type 1: Regular grouped data table with an extra cumulative frequency column

This is the most common way you'll see it:

Type 2: Relabeled table starting from zero

In this version, each row shows the cumulative frequency "up to" a certain value, rather than "in the range":

Converting between the two: If you have Type 2, you can find individual frequencies by subtracting:

• Frequency of 20 ≤ x < 40 = 39 − 14 = 25
• Frequency of 40 ≤ x < 60 = 68 − 39 = 29

Drawing Cumulative Frequency Diagrams

Interpreting Cumulative Frequency Diagrams

Common Mistakes to Avoid