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First: put the data into ascending order.

1, 1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 8, 8, 9, 13, 24, 25

MIN: 1; MAX: 25
MEDIAN: 4. This is the 50th percentile, and divides the data into two sets each containing half the results.

Set 1: 1, 1, 1, 1, 2, 2, 3, 4

Set 1 median: 1.5 (average of middle data)

Set 2: 5, 6, 8, 8, 9, 13, 24, 25

Set 2 median: 8.5
The medians split the data into 4 groups or quartiles: <1.5; >1.5 but <=4; >4 but <8.5; >8.5. Data <1.5 or >8.5 are called outliers.

Draw a vertical line representative no the data and mark the limits 1 and 25 on the line. These are the bottom and top of the box. Now mark the medians at 1.5, 4 and 8.5. These form an inner box with 1.5 as its bottom and 8.5 as its top, with 4 sandwiched inside. Draw horizontal lines to show the boxes. These horizontal lines are of no specific length. That's your box plot. You can use colours or shading in the inner box to show the data between the three medians (data between 1.5 and 8.5), and the outliers will be in the larger outer box in an unshaded area.

by Top Rated User (717k points)

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