What it shows
A box and whisker plot with whiskers drawn to the smallest and largest values. The box marks the first quartile, the median and the third quartile; no point is set apart as an outlier, so the plot shows the five-number summary and nothing else.
It uses the same 20 values as the box plot with an outlier. The box is identical in both; only the upper whisker differs.
How to read it
Read the five-number summary from the bottom up: minimum 12, Q1 21, median 27, Q3 33, maximum 58.
The box holds the middle half of the data. Its height, 12, is the interquartile range.
The long upper whisker reflects a single high value. In the outlier version of this plot, drawn by Tukey’s rule, the same value, 58, is plotted on its own.
The numbers behind it
- Data (n = 20): 12, 15, 17, 18, 21, 21, 22, 24, 25, 26, 28, 29, 30, 31, 33, 33, 35, 38, 41, 58.
- Minimum = 12, Q1 = 21, median = 27, Q3 = 33, maximum = 58, IQR = 12.
- Tukey’s hinges and Hyndman and Fan types 6 and 7 give the same quartiles for these data.
Ways to use it in teaching
Ask what this version cannot show: whether 58 is an error, a rare case or part of a long tail.
Set it beside the outlier version and discuss which belongs in a results chapter.
Introduce box plots with this one, before the 1.5 × IQR rule.
For the summary statistics behind this kind of chart, see our plain-language guide to descriptive statistics.
Sources
Tukey, J. W. (1977), Exploratory Data Analysis, Addison-Wesley (the box-and-whisker plot); Hyndman, R. J. and Fan, Y. (1996), "Sample quantiles in statistical packages", The American Statistician 50(4): 361–365 (the quantile types).
