Histograms

A histogram looks like a bar chart, except the area of the bar, and not the height, shows the frequency of the data. Histograms are typically used when the data is in groups of unequal width.

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

AgeFrequency
5-106
11-1515
16-174

Each class, or category, is not equally sized, which is typical in a histogram question. This is called unequal class intervals.

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

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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