Creating a cumulative frequency histogram, often referred to as an ogive, involves several key steps. Unlike a regular histogram, a cumulative frequency histogram displays the running total of frequencies, showing how many data points fall below a certain value.
Here's a step-by-step guide:
1. Calculate Cumulative Frequencies
First, you need to determine the cumulative frequency for each class interval. This is done by adding the frequency of each interval to the sum of the frequencies of all the intervals before it.
Example:
Let's say you have the following frequency distribution table:
| Class Interval | Frequency |
|---|---|
| 10-20 | 5 |
| 20-30 | 8 |
| 30-40 | 12 |
| 40-50 | 7 |
To calculate the cumulative frequencies:
| Class Interval | Frequency | Cumulative Frequency |
|---|---|---|
| 10-20 | 5 | 5 |
| 20-30 | 8 | 5 + 8 = 13 |
| 30-40 | 12 | 13 + 12 = 25 |
| 40-50 | 7 | 25 + 7 = 32 |
2. Set Up the Axes
Next, create a graph with the x-axis representing the class intervals and the y-axis representing the cumulative frequency.
- X-axis: Label the x-axis with the upper class boundaries of each interval (e.g., 20, 30, 40, 50 in the example above). You'll also want to include the lower boundary of the first interval (e.g., 10).
- Y-axis: Label the y-axis with cumulative frequencies, choosing a scale that accommodates the maximum cumulative frequency value.
3. Plot the Points
Plot each cumulative frequency value at the upper boundary of its corresponding class interval.
- For the example above, you would plot the points (20, 5), (30, 13), (40, 25), and (50, 32). Additionally, plot (10, 0) to show that there are zero values below the first interval's lower bound.
4. Connect the Points
Draw a smooth curve or a series of straight lines to connect the plotted points. This curve is the cumulative frequency polygon (or ogive). Start the curve at the point corresponding to the lower boundary of the first class interval with a cumulative frequency of zero.
5. Add a Title and Labels
Finally, add a descriptive title to the graph and label the axes clearly so the cumulative frequency histogram is easily understood.
Example:
"Cumulative Frequency Histogram of Test Scores"
Summary:
To make a cumulative frequency histogram, calculate cumulative frequencies, set up axes representing class intervals and cumulative frequencies, plot the cumulative frequency at the upper boundary of each class interval, connect the points with a smooth curve or lines, and add a title and labels. This will create a graphical representation showing the number of data points falling below certain values.
