大象传媒

Histograms

A histogram looks like a , except the area of the bar, and not the height, shows the frequency of the . 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
Age5-10
Frequency6
Age11-15
Frequency15
Age16-17
Frequency4

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
Age5-10
Frequency6
Class width6 (5, 6, 7, 8, 9 and 10 are in this category)
Age11-15
Frequency15
Class width5
Age16-17
Frequency4
Class width2

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\(4 \div 2 = 2\)
Age5-10
Frequency6
Class width6 (5, 6, 7, 8, 9 and 10 are in this category)
Frequency density\(6 \div 6 = 1\)
Age11-15
Frequency15
Class width5
Frequency density\(15 \div 5 = 3\)
Age16-17
Frequency4
Class width2
Frequency density\(4 \div 2 = 2\)

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

Histogram of age vs frequency density