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# How to Find Class Midpoints in a Frequency Distribution

A frequency distribution table is a table that displays the frequencies of different data classes.

For example, the following frequency distribution table shows the frequency for five different classes:

Class Frequency
1 â€“ 10 20
11 â€“ 20 21
21 â€“ 30 16
31 â€“ 40 5
41 â€“ 50 4

You can find the midpointÂ of each class by adding the lower class limit and the upper class limit, then dividing by two:

Class midpointÂ  = (lower class limit + upper class limit) / 2

The following table shows how to calculate the midpoint of each class:

Class Frequency Midpoint
1 â€“ 10 20 (1+10) / 2
11 â€“ 20 21 (11+20) / 2
21 â€“ 30 16 (21+30) / 2
31 â€“ 40 5 (31+40) / 2
41 â€“ 50 4 (41+50) / 2

Thus, weâ€™re left with the following midpoints:

Class Frequency Midpoint
1 â€“ 10 20 5.5
11 â€“ 20 21 15.5
21 â€“ 30 16 25.5
31 â€“ 40 5 35.5
41 â€“ 50 4 45.5

## When Are Class Midpoints Used?

Class midpoints are often used when you want to create a histogram to visualize the values in a frequency table.

A histogram lists the classes along the x-axis of a graph and uses bars to represent the frequency of each class along the y-axis. Each bar is centered at itsÂ class midpoint.Â

The following histogram provides a visual representation of the data in the previous frequency table:

Notice how each bar is centered at its class midpoint:

When youâ€™re creating a histogram by hand, itâ€™s especially useful to know the class midpoints so that you know where to place the bars.

However, most statistical softwares are able to automatically center the bars of a histogram around the class midpoints, so you typically wonâ€™t have to manually find these midpoints yourself.