Histograms

On a histogram, the area of the bar, and not the height, represents the frequency of the data. Histograms are typically used when the data is in groups.

The table shows the ages of 25 children on a school trip.

AgeFrequency
5-106
11-1515
16-174

To draw a histogram for this information, first find the class width of each category.

AgeFrequencyClass width
5-1066 (5, 6, 7, 8, 9 and 10 are in this category)
11-15155
16-1742

When class widths are not equally sized, they are called unequal class intervals.

The area of the bar represents the frequency, so to find the height of the bar, divide frequency by the class width. This is called frequency density.

AgeFrequencyClass widthFrequency density
5-1066 (5, 6, 7, 8, 9 and 10 are in this category) 6 \div 6 = 1
11-15155 15 \div 5 = 3
16-1742 4 \div 2 = 2

Once the frequency densities of the numbers are known, the histogram can be drawn.

Histogram of age vs frequency density
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