What Does a Grouped Frequency Table Look Like?
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A table of intervals is a frequency table where the data you’ve found is grouped into intervals. This is also called a grouped table of frequencies. The data is grouped in a way that seems natural. For example, if you’re dealing with weights, it’s natural to group the data into rounded intervals, such as 16–20kg, 21–25kg, and so on.
If you were working with a situation where you can count individual observations, like letter grades on an exam, you wouldn’t choose a table of intervals for the task. In that case, a frequency table is the right way to go. In Example 1 below, we’re looking at the weight of a group of skaters.
Theory
Values for Tables of Intervals
| Interval limits |
| from and including to |
| from through |
| Interval width |
| Midpoint of interval |
| Interval limits: | from and including to |
| from through | |
| Interval width: | |
| Midpoint of interval: | |
Example 1
A group of skaters are distributed into different weight classes. Here’s a table showing the classes and the frequency of each class.
| Weight (kg) | Frequency |
| 7 | |
| 8 | |
| 12 | |
| 9 | |
| 6 | |
By summing the values in the column containing the frequencies, we can see that there are 42 skaters in total. You can find the limits of the intervals in the column containing the weights. You can see that the number on the left side of the interval, for example 55, is included in the interval. The number to the right in the interval, for example 60, is not included in the interval, it’s included in the next interval instead. From that you get:
The midpoint for the first interval is:
