Method

Drawing a Histogram

Some data sets can be illustrated with a histogram. Consider the following data set. 13, 11, 4, 11, 21, 25, 37, 17, 8, 19, 26, 15 To draw a histogram for this data set, there are four steps to follow.

Choose the Number of Intervals

The first step to drawing a histogram is deciding how many intervals it will have. Remember that each interval must be the same length and all data points must lie within one of intervals. First, count the number of data points in the set. cccccccccccc 13, & 11, & 4, & 11, & 21, & 25, 1 & 2 & 3 & 4 & 5 & 6 [0.2cm] 37, & 17, & 8, & 19, & 26, & 15 7 & 8 & 9 & 10 & 11 & 12 One method to finding a suitable number of intervals is to take the square root of the number of data points. Since there are 12 numbers in the data set, calculate the square root of 12. sqrt(12)=3.464101... This means that the histogram can have either three or four intervals. This example histogram will use four intervals.

Determine the Size of the Intervals

Determine the size of the intervals. Start by identifying the lowest and highest data value in the set. Lowest:& 4 Highest:& 37 Since the lowest data value in the set is 4 and the highest is 37, using four intervals with a range of 10 will cover the numbers from 1 to 40 and, therefore, will encompass all data points. The intervals of the histogram will be the following. 1 -- 10, 11 -- 20, 21 -- 30, 31 -- 40

Make a Frequency Table

The next step is to make a frequency table showing how many data points lie in each interval.

Interval	Data Points	Frequency
1-10	4, 8	2
11-20	11, 11, 13, 15, 17, 19	6
21-30	21, 25, 26	3
31-40	37	1

Draw the Histogram

The histogram can be constructed by drawing a bar over each interval with a height corresponding to the frequency listed in the table.

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