Constructing a Cumulative Frequency Distribution

Oct 13, 2025 by pynkocean.com 60 views

Introduction

In statistics, a cumulative frequency distribution is a table or graph that shows the number of observations that fall below a certain value. It is a useful tool for understanding the distribution of data and identifying patterns or trends. In this article, we will learn how to construct a cumulative frequency distribution with 6 classes.

What is a Cumulative Frequency Distribution?

A cumulative frequency distribution is a table or graph that shows the number of observations that fall below a certain value. It is a cumulative sum of the frequencies of the data points. For example, if we have a dataset of exam scores, a cumulative frequency distribution would show the number of students who scored below a certain score.

Why is a Cumulative Frequency Distribution Important?

A cumulative frequency distribution is important because it helps us to understand the distribution of data. It can be used to identify patterns or trends in the data, such as the presence of outliers or skewness. It can also be used to calculate the median and quartiles of the data.

Constructing a Cumulative Frequency Distribution

To construct a cumulative frequency distribution, we need to follow these steps:

Step 1: Determine the Classes

The first step in constructing a cumulative frequency distribution is to determine the classes. In this example, we will use 6 classes:

Less than 89.5
Less than 98.5
Less than 107.5
Less than 116.5
Less than 125.5
Less than 134.5

Step 2: Create a Table or Graph

The next step is to create a table or graph to display the cumulative frequency distribution. We will use a table for this example.

Class	Frequency	Cumulative Frequency
Less than 89.5
Less than 98.5
Less than 107.5
Less than 116.5
Less than 125.5
Less than 134.5

Step 3: Fill in the Frequencies

The next step is to fill in the frequencies for each class. For example, if we have a dataset of exam scores, we would count the number of students who scored below each of the class boundaries.

Class	Frequency	Cumulative Frequency
Less than 89.5	10	10
Less than 98.5	20	30
Less than 107.5	30	60
Less than 116.5	40	100
Less than 125.5	50	150
Less than 134.5	60	210

Step 4: Calculate the Cumulative Frequency

The final step is to calculate the cumulative frequency for each class. This is done by adding the frequency of each class to the cumulative frequency of the previous class.

Class	Frequency	Cumulative Frequency
Less than 89.5	10	10
Less than 98.5	20	30
Less than 107.5	30	60
Less than 116.5	40	100
Less than 125.5	50	150
Less than 134.5	60	210

Interpreting the Cumulative Frequency Distribution

The cumulative frequency distribution shows the number of observations that fall below each of the class boundaries. It can be used to identify patterns or trends in the data, such as the presence of outliers or skewness. It can also be used to calculate the median and quartiles of the data.

Conclusion

In this article, we learned how to construct a cumulative frequency distribution with 6 classes. We also learned how to interpret the cumulative frequency distribution and how it can be used to identify patterns or trends in the data. By following these steps, you can create a cumulative frequency distribution for your own dataset and gain a better understanding of the distribution of your data.

Example Use Case

A teacher wants to understand the distribution of exam scores in her class. She collects the scores and creates a cumulative frequency distribution with 6 classes:

Less than 89.5
Less than 98.5
Less than 107.5
Less than 116.5
Less than 125.5
Less than 134.5

She fills in the frequencies for each class and calculates the cumulative frequency. The resulting table shows the number of students who scored below each of the class boundaries.

Class	Frequency	Cumulative Frequency
Less than 89.5	10	10
Less than 98.5	20	30
Less than 107.5	30	60
Less than 116.5	40	100
Less than 125.5	50	150
Less than 134.5	60	210

The teacher can use this table to identify patterns or trends in the data, such as the presence of outliers or skewness. She can also use it to calculate the median and quartiles of the data.

Code Example

Here is an example of how to create a cumulative frequency distribution in Python:

import pandas as pd

# Create a sample dataset
data = {
    'Score': [85, 92, 105, 115, 125, 135]
}

# Create a pandas DataFrame
df = pd.DataFrame(data)

# Create a cumulative frequency distribution
df['Cumulative Frequency'] = df['Score'].cumcount() + 1

# Print the resulting table
print(df)

This code creates a sample dataset and calculates the cumulative frequency for each score. The resulting table shows the number of students who scored below each of the class boundaries.