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The process of finding the class midpoints in a frequency distribution involves several steps. First, the range of the data must be determined by subtracting the lowest value from the highest value. Next, the range is divided by the desired number of classes to determine the interval size. The starting point for the first class is then chosen, typically by rounding down to the nearest multiple of the interval size. From this starting point, the class midpoints can be calculated by adding half of the interval size to each successive class boundary. These class midpoints represent the average value of each class and are used to create a visual representation of the data in a frequency distribution.
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 – 10 | 20 |
| 11 – 20 | 21 |
| 21 – 30 | 16 |
| 31 – 40 | 5 |
| 41 – 50 | 4 |
You can find the midpoint of each class by adding the lower class limit and the upper class limit, then dividing by two:
Class midpoint = (lower class limit + upper class limit) / 2
The following table shows how to calculate the midpoint of each class:
| Class | Frequency | Midpoint |
|---|---|---|
| 1 – 10 | 20 | (1+10) / 2 |
| 11 – 20 | 21 | (11+20) / 2 |
| 21 – 30 | 16 | (21+30) / 2 |
| 31 – 40 | 5 | (31+40) / 2 |
| 41 – 50 | 4 | (41+50) / 2 |
Thus, we’re left with the following midpoints:
| Class | Frequency | Midpoint |
|---|---|---|
| 1 – 10 | 20 | 5.5 |
| 11 – 20 | 21 | 15.5 |
| 21 – 30 | 16 | 25.5 |
| 31 – 40 | 5 | 35.5 |
| 41 – 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 its class midpoint.
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 you’re creating a histogram by hand, it’s especially useful to know the class midpoints so that you know where to place the bars.