**Understanding Cumulative Frequency and Cumulate Frequency Curves**

Cumulative frequency is a concept that is used in multiple disciplines, including research psychology, to help data analysts determine the total frequency of some sort of occurrence up to a given value. Finding cumulative frequency would be useful, for example, if a researcher collected the IQ scores of a group of college students and wanted to know how often students earned a score of 119 or lower.

Cumulative frequency can be graphically represented in several ways, but is most commonly shown through a cumulative frequency curve. Cumulative frequency curves look very similar to line graphs, and help analysts visualize information and predict future trends in data.

**Things You'll Need:**

- Writing utensil
- Calculator (optional)
- Paper
- Ruler or other straight edge
- Dataset

## Step 1: Place Frequency Data Into a Table

This will help you organize your frequency information. You will need to:

- Identify your measurement interval categories.
- Place frequency data into the cells below the appropriate intervals.

Let’s say, for example, you wanted to input frequency information about the amount of sleep 15 of your friends got last night into a table. Your friends report that they slept 6, 4, 11, 8, 9, 3, 5, 6, 6, 7, 8, 4, 2, 7, and 4 hours. Look to **Figure 1** to see how these data would be represented in a frequency table.

## Step 2: Find Cumulative Frequency of Each Interval and Input It Into a Table

- To find the cumulative frequency of each interval, locate the frequency score of the interval and add to it all frequency scores falling before it.
- Place cumulative frequency data into a row of cells below the frequency cells.

Look to **Figure 2** to see how the data from the example presented in Step 1 would look in a cumulative frequency table.

## Step 3: Set Up Your Plane for the Cumulative Frequency Curve

- Draw one vertical and one horizontal axis using your ruler or other straight edge.
- Label the vertical axis "Cumulative Frequency" and section it off into evenly spaced segments. The scale you use to section off the axis will depend on the range of your frequency data, but will always begin with 0.
- Label the horizontal axis as the measurement you're taking and section it off into segments that reflect your measurement intervals. Each segment should be labeled in accordance with the higher number of the interval being represented.

**Figure 3** shows how a plane for the sleep example would be drawn.

## Step 4: Plot and Connect Cumulative Frequency Data Points

- Plot each cumulative frequency data point on your plane with a small "x".
- Connect consecutive points together with straight lines with the help of your ruler or other straight edge.

**Figure 4** shows how the cumulative frequency data points would be plotted and connected for the sleep example.

## Step 5: Interpret Your Cumulative Frequency Table and Curve

Use the cumulative frequency table and curve to learn more about your data.

Going back to the sleep example, you may wonder how many of your friends slept 7 hours or less last night. To find out, you should look to the cumulative frequency number under the “6-7 hours” category of your cumulative frequency table. This will reveal that 11 of your friends got 7 hours or less of sleep last night.

Looking at your cumulative frequency curve will help you visualize and notice new things about your data. In the sleep example, you may notice a sharp increase from the 3-hour mark to the 7-hour mark. This demonstrates that the majority of your friends got 3 to 7 hours of sleep last night.