Five-number Summary Definition
"Five-number summary" refers to "minimum value", "first quartile", "median", "third quartile", and "maximum value".
Different software generally have the same results for "minimum value", "median", and "maximum value", but there are different ways to get "first quartile" and "third quartile".
"Minimum value" can also be referred as "Q0".
"First quartile" can also be referred as "Q1", "lower quartile", "lower hinge", or "25th percentile".
"Median" can also be referred as "Q2" or "second quartile".
"Third quartile" can also be referred as "Q3", "upper quartile", "upper hinge", or "75th percentile".
"Maximum value" can also be referred as "Q4".
Tukey's hinge method includes median in the first/third quartile calculation, TI-83 & TI-84 & TI-89 method excludes median in the first/third quartile calculation. The percentile method is based on the default used in the statistical software S and R.
Five-number Summary Example
This calculator will provide the five-number summary results based on three most popular methods, as explained below.
For "1,2,3,4,5,6,7", the minimum is 1, the median is 4, the maximum is 7.
If Tukey's hinge method is used, the "first quartile" is 2.5 which is the median of "1,2,3,4", and the "third quartile" is 5.5 which is the median of "4,5,6,7".
If TI-83 & TI-84 & TI-89 method is used, the "first quartile" is 2 which is the median of "1,2,3", and the "third quartile" is 6 which is the median of "5,6,7".
As the length of 7 is an odd number, the percentile method produces the same result as Tukey's hinge method.
For "1,2,3,4,5,6", the minimum is 1, the median is (3+4)/2=3.5, the maximum is 6.
If Tukey's hinge method is used, the "first quartile" is 2 which is the median of "1,2,3", and the "third quartile" is 5 which is the median of "4,5,6".
As the length of 6 is an even number, the TI-83 & TI-84 & TI-89 method produces the same result as Tukey's hinge method.
For the percentile method, it is calculated with the minimum value of 1 as the 0th percentile and the maximum value of 6 as the 100th percentile. Therefore, the 25th percentile is 1+(6-1)*0.25=2.25, and the 75th percentile is 1+(6-1)*0.75=4.75.