how to find the cumulative frequency

Daniel Parker

2 min read

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15-03-2025

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Cumulative frequency is a running total of frequencies. It shows the total number of observations up to a certain point in a dataset. Understanding how to calculate it is crucial in statistics for interpreting data and creating visual representations like cumulative frequency curves (ogives). This guide will walk you through the process, providing clear examples.

Understanding Frequency and Cumulative Frequency

Before diving into calculations, let's clarify the terms:

• Frequency: The number of times a specific value or range of values appears in a dataset. For instance, if 5 students scored 80% on a test, the frequency of 80% is 5.

• Cumulative Frequency: The sum of frequencies up to a given point. It's a running total, adding each frequency to the previous one. It helps visualize the distribution of data, showing how many observations fall below a certain value.

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

Let's illustrate with an example. Suppose we have the following data representing the number of hours students spent studying for an exam:

Here's how to calculate the cumulative frequency:

Step 1: Create a table with an additional column for Cumulative Frequency.

Step 2: Calculate the cumulative frequency for each row.

• Row 1: The cumulative frequency for the first row is simply the frequency of that row (3).

• Row 2: Add the frequency of the second row (5) to the cumulative frequency of the previous row (3). 3 + 5 = 8.

• Row 3: Add the frequency of the third row (7) to the cumulative frequency of the previous row (8). 8 + 7 = 15.

• Row 4: Add the frequency of the fourth row (4) to the cumulative frequency of the previous row (15). 15 + 4 = 19.

• Row 5: Add the frequency of the fifth row (1) to the cumulative frequency of the previous row (19). 19 + 1 = 20.

Step 3: Complete the table.

The completed table will look like this:

The final cumulative frequency (20) represents the total number of students in the dataset.

Cumulative Frequency for Individual Data Points

If you have individual data points instead of grouped data (like in our example above), the process is similar but slightly simpler. Let's say we have the following data set:

2, 5, 2, 8, 1, 5, 9, 2, 6, 7

Step 1: Order the data: First, arrange the data in ascending order: 1, 2, 2, 2, 5, 5, 6, 7, 8, 9

Step 2: Create a frequency table:

The cumulative frequency is calculated in the same way as before—a running total of the frequencies.

Applications of Cumulative Frequency

Cumulative frequency is a valuable tool in various statistical applications:

• Creating ogives (cumulative frequency curves): These curves provide a visual representation of the distribution of data.
• Finding percentiles and quartiles: Cumulative frequency allows for easy calculation of these descriptive statistics.
• Understanding data distribution: It helps to understand how data is spread across different ranges.

By following these steps, you can confidently calculate cumulative frequency for any dataset, whether grouped or individual data points. Remember to always organize your data and proceed systematically for accurate results.