Cumulative Frequency: In statistics, cumulative frequency is defined as the sum of frequencies distributed across various class intervals. This involves organizing the data and their totals into a table where the frequencies are allocated according to each class interval.

In this article, we will cover a thorough explanation of cumulative frequency, cumulative frequency curve, formula, and a few examples based on it for better understanding.

What is Cumulative Frequency?

Cumulative Frequency is the sum of all previous frequencies of the given data. Consider the frequency of the first class interval plus the frequency of the second class interval, the sum is then added to the frequency of the third class interval, and so on, to get the cumulative frequency. Therefore, the cumulative frequency table, also known as the cumulative frequency distribution, is the table that shows the cumulative frequencies that are split over various classes.

In most cases, the number of observations in the given data set that fall above or below a specific frequency is determined using the cumulative frequency distribution.

Cumulative Frequency Meaning

Cumulative frequency (c.f.) is the term used to determine the total number of observation above the current point, irrespective of the class of the given dataset. In simple terms, it is the sum of all previous observation of the given data.

Cumulative frequency is classified into two types: lesser than type and greater than type. The number of observations in a given data set that fall above (or below) a specific frequency is determined using cumulative frequency.

Cumulative Frequency Formula

The frequencies of all the data points that are equal to or less than a given value are added up to determine the cumulative frequency (CF) at that particular data point. In terms of math, it is expressed as:

[Tex]CF_i = \sum_{j=1}^{i} f_j [/Tex]

​where,

• CF_i is Cumulative Frequency at the i^th Data Point
• F_j is the j^th Data Point’s Frequency

Cumulative Frequency Distribution

Cumulative Frequency Distribution is a technique used in statistics for data organization and analysis. To create a cumulative frequency table, the frequencies of each data point are added up to a specific value. This table makes it easy to understand how many observations in the dataset fall below or equal to a given point.

When comparing various data sets, determining central tendencies, and visualizing the overall pattern of the data, the cumulative frequency distribution is especially helpful. It is frequently used in statistical analysis to learn more about the properties and distribution of a dataset.

Types of Cumulative Frequency

Cumulative Frequency are classified into two types namely:

• Less than Cumulative Frequency
• More than Cumulative Frequency

Less than Cumulative Frequency

Less than cumulative frequency, also known as a less than ogive, is a rising curve. It is obtained by adding the first-class frequency to the second-class frequency, and so on. Here, the cumulate begins from the lowest to the highest class.

In this frequency curve, the points are plotted using upper limits (x-axis) and their corresponding cumulative frequency (y-axis).

More than Cumulative Frequency

More than cumulative frequency, also known as a greater than cumulative frequency, is a downward curve. It is obtained by determining the cumulative total frequencies starting from the last class to the first class. Here, the cumulate begins from the highest to the lowest class.

In this frequency curve, the points are plotted using lower limits (x-axis) and their corresponding cumulative frequency (y-axis).

How to Calculate Cumulative Frequency?

Cumulative frequency is a statistical method that can be used to organize and examine data. It involves adding up all of the values of frequencies cumulatively within a dataset. Here’s a step-by-step explanation to find the cumulative frequency of the given dataset:

Step 1: Organize Data

To get started, form the dataset into ascending or descending order.

Step 2: Create a Frequency Table

Make a frequency table with the Value column and Frequency column then List all unique values in the dataset and their corresponding frequency.

Step 3: Add Cumulative Frequencies

Create a new column labeled “Cumulative Frequencies” in the frequency table. The cumulative frequency for the first row is the same as the frequency. Add the current row’s frequency to the previous row’s cumulative frequency for each subsequent row.

Example: Creating a Cumulative Frequency table with the below values and frequencies