What inferences about probability can I glean from a box and whisker plot?

1 Answer
Oct 13, 2016

A box and whisker plot should tell you the median value of your dataset, the maximum and minimum values, the range in which 50% of values fall and the values of any outliers.

Explanation:

More technically, you can regard a box and whisker plot in terms of quartiles.

The top whisker is the maximum value, the bottom whisker the minimum value (assuming neither of the values are outliers (see below)).

Information on probabilities is gleaned from the positions of quartiles.
The top of the box is Q1, the first quartile. 25% of values lie below Q1.
Somewhere inside the box will be Q2. 50% of values lie below Q2. Q2 is the median of the dataset.
The bottom of the box is Q3. 75% of values lie below Q3.

Q3 - Q1 (the length of the box) is the interquartile range, in which 50% of values lie.

If a value falls above Q3 + 1.5 (\text{IQR}) or below Q1 - 1.5 (\text{IQR}), it is classified a suspected outlier and will be marked with a circle on the box and whisker plot. If it falls above Q3 + 3 (\text{IQR}) or below Q1 - 3 (\text{IQR}) it is classified an outlier and marked with a solid circle.

For examples, see

www.physics.csbsju.eduwww.physics.csbsju.edu

and

www.physics.csbsju.eduwww.physics.csbsju.edu

These images are from this descriptive, useful page that you should read for further explanation and more examples.

These Wikipedia pages on quartiles, interquartile range and box and whisker plots should be useful also
Quartiles
Interquartile range
Box and whisker plots