# Cumulative frequency distribution

< List of probability distributions < Cumulative frequency distribution

A cumulative frequency distribution is an important tool for data analysis. It’s a way to show the sum of all values up to the current class in a frequency distribution. If you’re familiar with spreadsheets, it’s a lot like using the SUM() function but for data sets instead of individual cells. In this blog post, we’ll explain what a cumulative frequency distribution is and how to use it.

## What is a Cumulative Frequency Distribution?

A cumulative frequency distribution (CFD) is the sum of all values up to and including the current class in a frequency distribution. This allows us to take several different classes and add them together into one value that represents all of them as a whole. For example, if we have three classes with frequencies of 5, 10, and 15 respectively, then our CFD would be 30 (5+10+15).

## How to Calculate Cumulative Frequency Distributions

Calculating cumulative frequency distributions can be time consuming if you don’t have the right tools. The easiest way to calculate CFDs is by using spreadsheet software such as Microsoft Excel or Google Sheets. In these programs, you can use the SUM() function (or its equivalent) to quickly sum up all of your classes into one value. This will save you time and give you more accurate results than if you were doing it by hand.

A simple calculation example: Mo gets paid \$250 each week. The second week they get paid \$300 and the third week, \$350. The cumulative amount for week 2 is \$550 (\$300 for week 2 and \$250 for week 1). The cumulative amount for week 3 is \$900 (\$350 for week 3, \$300 for week 2 and \$250 for week 1).

Example question: What is the value for ? in the following cumulative distribution table?

Solution: 41. To get this number, add up all of the frequencies in the second column (freq), stopping when you get to the third row (which is where the “?” is placed):
15 + 10 + 16 = 41.

## Make a cumulative frequency distribution table

Example question: Make a cumulative frequency distribution table for the following data, Use 7 classes: 1, 6, 9, 11, 12, 13, 14, 21, 21, 23, 26, 27, 28, 29, 29, 31, 31, 32, 33, 34, 35, 36 .

1: Draw a table and label column 1 with class widths. In column 2, count the number of items in each class and fill the columns.

2: Calculate the cumulative frequencies. The first entry will equal first entry in the frequency column. The second entry will be the sum of the first two entries in the frequency column (highlighted in red).

## Uses for Cumulative Frequency Distributions

Cumulative frequency distributions are useful for analyzing data sets because they allow us to quickly see how much of something has been accumulated over time. For example, if we had sales figures from each month over the course of one year, we could use CFDs to get an idea of how much total sales we had at any given point in time without having to manually add up each month’s numbers individually. This type of analysis can help us make decisions about our business strategy and determine where changes need to be made in order to maximize profits.

You can also use cumulative frequency distributions to check that your math is correct. By summing the totals and comparing it to a sample size, this confirms your calculations are right. For example if your sample size was 30 and your cumulative frequency is 29, you’d know that you’re missing one piece of data (which tells you to check your math!).

These distributions can also help with “more” or “less” questions. For example, you’re thinking of opening a bargain gaming store and you want to know how many people in your city spend up to \$2000 per person per year on gaming equipment (including computers). Your table might look like this:

The “Cum.freq” column tells you that 6700 people spend up to \$2,000 per year on gaming. The fact that most people are willing to spend more signals that you may be better off opening a mid-priced store, instead of a bargain one.

## TI-89

Q: Build a cumulative frequency table for the following data:

1. Install the Stats/List Editor.
2. Press APPS and scroll to Stats/List Editor. Press ENTER.
3. Press F1 8 to clear data in the editor.
4. Enter 4 1. This names the first column “L1
5. Enter your values into L1, following each number by an Enter key:
• 1 ENTER
• 2 ENTER
• 4 ENTER
• 0 ENTER
• 3 ENTER
• 5 ENTER
• 6 ENTER.
6. Move your cursor to on the header for column 2 (the column header will be highlighted). Press ALPHA 4 2 to name the column “L2.” Press ENTER. Use the up arrow to highlight the column header (L2).
7. Press F3 2 6 to get the cumsum( function.
8. Enter “L1” into the cumsum function by pressing ALPHA 4 1. Press the ) key then press ENTER.
9. The list of cumulative frequencies for each value in L1 are returned in L2: 1, 3, 7, 7, 10, 15.

The TI-83 is similar, except you do not have to install the Stats/List editor (the TI-83 is pre-loaded for statistics function).

## Conclusion

Cumulative frequency distributions are an invaluable tool for data analysis and business decision-making alike. Understanding how CFDs work and how they can be used can help businesses take their data-driven decisions to new heights. With just a bit of practice and some spreadsheet software, anyone can easily create their own CFDs and start making smarter decisions based on their data sets.