Frequency Distributions and Visualizing Data

Cumulative Frequency Distribution

 Learning Objectives

Construct and understand cumulative frequency distributions

A cumulative frequency distribution is:

  • A running total of the frequencies and relative percent frequencies
  • Useful for understanding the percentiles in the data
  • Will be useful for creating type of chart called an ogive
  • See the sample cumulative frequency table below (based on the 2019 student survey data):
Heights (cms) Cumulative Frequency Cumulative % Frequency
< 143 0 0.%
< 150 1 0.57%
< 157 14 8.00%
< 164 46 26.29%
< 171 93 53.14%
< 178 119 68.00%
< 185 163 93.14%
< 192 172 98.29%
< 199 175 100%

How to Construct Cumulative Frequency Distributions

To construct a cumulative frequency table, follow the following steps:

  1. First, construct the frequency table (see the previous section)
  2. Start your cumulative frequency table at zero (below your first lower limit)
  3. Next, start totaling up the frequencies: [latex]\text{Cumul Freq} = \text{Previous Cumul Freq} + \text{Current Freq}[/latex]
  4. Finally, divide each of the cumulative frequencies by the total number of data (sample size) to calculate the cumulative % (relative) frequencies: \[ \text{Cumulative % Frequency} = \frac{\text{Cumulative Frequency}}{\text{Sample Size}} \]

Creating Frequency Tables ‘Manually’ (EXERCISE)

Example 10.1.1

Problem Setup: Let us revisit the sample of 30 BCIT students. See the frequency table created for this data from the previous section:

  Class Frequency % Frequency
  143 – 149 1 0.57%
  150 – 156 13 7.43%
  157 – 163 32 18.29%
  164 – 170 47 26.86%
  171 – 177 26 14.86%
  178 – 184 44 25.14%
  185 – 191 9 5.14%
  192 – 198 3 1.71%
Totals 175 100%

Question: Can you create the cumulative frequency distribution for this data? Drag and drop the values into the correct positions below to create the cumulative frequency table.

Solution: Need help? See the solutions below:

Creating Cumulative Frequency Tables using pivot tables (VIDEO)

Example 10.1.2

Problem Setup: Let us now revisit the 30 students’ heights example from the previous section, but this time, using a Pivot Table in Excel. Click here to download the file shown in the video below.

Solution: Click here to download the solution file.

Key Takeaways (EXERCISE)

Key Takeaways: Cumulative Frequency Distributions

Your Own Notes (EXERCISE)

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An Introduction to Business Statistics for Analytics (1st Edition) Copyright © 2024 by Amy Goldlist; Charles Chan; Leslie Major; Michael Johnson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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