# How to Calculate Frequency Density

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A histogram compares grouped continuous data. If, for example, you wanted to compare the number of widgets produced in the U.S. throughout the 20th century. You might use a histogram, and each bar would represent a range of dates. 1900 to 1909 might be your first bar. Your second might be 1910 to 1919. If all these bars represent a 10-year interval, then every bar would have the same width. If you wanted to illustrate a difference in production during the first half of the next decade compared to the second half, your next two bars would be half as wide as the first two. To meaningfully compare the amount of production in different time intervals, you would need to use frequency density.

• Determine whether or not your bars are of the same or different widths. If they are all the same, then there is no reason to calculate frequency density, and simple representation of frequency will be sufficient. If some are wider than others, then frequency density will be a more useful way to represent the data.

• Divide the frequency by the width of the bar. Suppose production in the chosen time intervals are as follows:

Period _ Widgets Frequency __ Frequency Density

1900-1909 _1200 _ 1200 ___ 120/year

1910-1919 _1000 _ 1000 ___ 100/year

1920-1924 900 __ 900 _____ 180/year

1925-1929 500 __ 500 _____ 100/year

In the first two time intervals, the frequency is higher. But the frequency density is highest in the third time interval, because the bar is only five years wide, instead of 10 years wide.

• Represent your data with frequency density on your y-axis rather than frequency. This will make it easier to see at a glance that production was higher in your third time intervals. A histogram illustrating frequency instead of frequency density would give a misleading picture.

## References

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