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Box and Whiskers Plot: Calculations Help

The calculations are summarized below. These calculations are based on the article “Quartiles: How to Calculate Them?” by David Journet. In particular, the program uses the SAS method 4 outlined in the paper.


The quartiles are calculated as shown below. The data below has been sorted in ascending order. There are 28 data points.

The program uses:

where p the percentile (0.25 for Q1 or .075 for Q3), n = number of data points, j is the integer portion of y, and g is the decimal portion of y.




The median is calculated using Excel’s built-in median function (Median).


The upper whisker is the largest value in the data set that is less than the upper limit = Q3 + 1.5(Q3 – Q1)

The lower whisker is the smallest value in the data set that is greater than the lower limit = Q1 – 1.5(Q3 – Q1)

Plot of Q1, Q3, Median, Whiskers and Outliers

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