Method

Drawing a Box Plot

A box plot can be used to display the distribution of a data set of numbers. To draw it, the minimum, maximum, median, and first and third quartiles of the data set need to be identified. The following data set gives the test scores of a particular class. 8.5, 11, 16, 12.5, 11, 15.5, 12, 7, 13, 10.5, 5, 15, 8, 9, 8, 8.5, 6 , 12, 15, 15.5, 13.5, 7.5, 13, 10.5, 11.5, 13.5 There are four steps to follow to draw a box plot for the data set.

Find the Minimum and Maximum

Sometimes, the data is given in sequential order. When it is not, it is necessary to start by ordering the data points from least to greatest. 5, 6, 7, 7.5, 8, 8, 8.5, 8.5, 9, 10.5, 10.5, 11, 11, 11.5, 12, 12, 12.5, 13, 13, 13.5, 13.5, 15, 15, 15.5, 15.5, 16 Now the minimum and maximum are easily identifiable in this ordered data set. Note that outliers can be ignored when determining the minimum and maximum. There are no outliers in this data set, so the minimum is 5 and the maximum is 16. These values are marked above a number line with two short vertical segments, indicating the range of the box plot.

Determine the Median

To find the median of the data set, count the number of values in the set. 1 5, 2 6, 3 7, 4 7.5, 5 8, 6 8, 7 8.5, 8 8.5, 9 9, 10 10.5, 11 10.5, 12 11, 13 11, 14 11.5, 15 12, 16 12, 17 12.5, 18 13, 19 13, 20 13.5, 21 13.5, 22 15, 23 15, 24 15.5, 25 15.5, 26 16 There are 26 values in the set. The median of a data set is the value that lies in the middle of the set. Since there are 26 values in this set, the median is the mean of the numbers in the 13th and 14th positions. 1 5, 2 6, 3 7, 4 7.5, 5 8, 6 8, 7 8.5, 8 8.5, 9 9, 10 10.5, 11 10.5, 12 11, 13 11, 14 11.5, 15 12, 16 12, 17 12.5, 18 13, 19 13, 20 13.5, 21 13.5, 22 15, 23 15, 24 15.5, 25 15.5, 26 16 ⇓ Median=11+11.5/2=11.25 The median is 11.25. Mark this value with a vertical line segment in the range above the number line. Remember that the line for the median will later appear inside the box.

Determine the Quartiles

The next step is to find the first and third quartiles of the data set. The median divides the set into two smaller sets, each with 13 values. Set1 1 5, 2 6, 3 7, 4 7.5, 5 8, 6 8, 7 8.5, 8 8.5, 9 9, 10 10.5, 11 10.5, 12 11, 13 11 [0.5em] Median: 11.25 [0.5em] 1 11.5, 2 12, 3 12, 4 12.5, 5 13, 6 13, 7 13.5, 8 13.5, 9 15, 10 15, 11 15.5, 12 15.5, 13 16 Set2 The first quartile is the median of the first set. Since there are 13 values in the set, the median is the 7th value, 8.5. Set1 1 5, 2 6, 3 7, 4 7.5, 5 8, 6 8, 7 8.5, 8 8.5, 9 9, 10 10.5, 11 10.5, 12 11, 13 11 The third quartile is the median of the second set. This will also be the 7th value, or 13.5. 1 11.5, 2 12, 3 12, 4 12.5, 5 13, 6 13, 7 13.5, 8 13.5, 9 15, 10 15, 11 15.5, 12 15.5, 13 16 Set2

Draw the Box Plot

The first and third quartiles are marked as the left and right sides of the box plot.

The box plot can be completed by drawing a box between the first and third quartiles Q_1 and Q_3. Then, the left and right borders of the box are connected by horizontal segments to the minimum and maximum.

The box plot is now complete.

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