Five Number Summary
There are a variety of descriptive statistics. Numbers such as the mean, median, mode, skewness,
and standard deviation, to name a few, each tell us something about our data. Rather than
looking at these descriptive statistics individually, sometimes combining them helps to give us a
more complete picture. With this end in mind, the five number summary is a convenient way to
combine five descriptive statistics. It is intended to help us know the center of our data, as well
as how spread out the data points are.
The five number summary consists of the following:
• The minimum – this is the smallest value in our data set.
• The first quartile – this number is denoted Q1 and 25% of our data falls below the first
quartile.
• The median – this is the midway point of the data. 50% of all data falls below the median.
• The third quartile – this number is denoted Q3 and 75% of our data falls below the third
quartile.
• The maximum – this is the largest value in our data set.
An Example
For the following set of 20 data points:
1, 2, 2, 3, 4,│6, 6, 7, 7, 7,│8, 11, 12, 15, 15,│15, 17, 17, 18, 20
A five number summary is:
Min
Q1
Med
Q3
Max
1 5 7.5 15 20
The mean and standard deviation can also be used together to convey the center and the spread
of a set of data. However, both of these statistics are susceptible to outliers. The median, first
quartile and third quartile are not as heavily influenced by outliers.
References:
http://statistics.about.com/od/Descriptive-Statistics/a/What-Is-A-Five-Number-Summary.htm
Hyndman, R. J. and Fan, Y. (1996) Sample quantiles in statistical packages, American
Statistician, 50:361–365
