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:
- First, construct the frequency table (see the previous section)
- Start your cumulative frequency table at zero (below your first lower limit)
- Next, start totaling up the frequencies: [latex]\text{Cumul Freq} = \text{Previous Cumul Freq} + \text{Current Freq}[/latex]
- 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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