how to find cumulative relative frequency

Daniel Parker

3 min read

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18-03-2025

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Understanding cumulative relative frequency is crucial in statistics for interpreting data and making informed decisions. This guide provides a clear, step-by-step process to calculate it, along with examples and helpful tips. We'll cover the basics and delve into more complex scenarios.

What is Cumulative Relative Frequency?

Cumulative relative frequency shows the proportion of observations that fall at or below a particular value in a dataset. It's expressed as a percentage or decimal. Unlike simple relative frequency (which shows the proportion at exactly a specific value), cumulative relative frequency considers the accumulation of values up to a certain point.

How to Calculate Cumulative Relative Frequency: A Step-by-Step Approach

Here's a breakdown of the process, illustrated with an example:

Step 1: Organize Your Data

Let's say we're analyzing the test scores of 20 students:

85, 92, 78, 88, 95, 82, 75, 90, 86, 92, 70, 80, 89, 94, 85, 72, 83, 91, 87, 79

First, arrange the data in ascending order:

70, 72, 75, 78, 79, 80, 82, 83, 85, 85, 86, 87, 88, 89, 90, 91, 92, 92, 94, 95

Step 2: Create a Frequency Distribution Table

Next, create a frequency distribution table. This table shows how many times each score appears.

Step 3: Calculate Relative Frequency

Divide each frequency by the total number of observations (20 in this case) to get the relative frequency.

Step 4: Calculate Cumulative Relative Frequency

Now, calculate the cumulative relative frequency. For each score, add its relative frequency to the sum of the relative frequencies of all preceding scores.

The final cumulative relative frequency should always equal 1 (or 100%).

Interpreting Cumulative Relative Frequency

The cumulative relative frequency tells us the proportion of data points that are less than or equal to a given value. For example, the cumulative relative frequency for a score of 85 is 0.50, meaning 50% of students scored 85 or below. This is valuable for understanding percentiles and identifying data distribution patterns.

Cumulative Relative Frequency for Grouped Data

The process for grouped data is similar. However, instead of individual scores, you work with class intervals. You'll need to find the relative frequency for each interval and then cumulatively add them up.

Remember to always organize your data, clearly label your table, and carefully calculate each step. Practicing with different datasets will help you master this essential statistical concept.