Five-Number Summary vs Quartile
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Five-number summary
Describing data
The five-number summary reports a data set's minimum, first quartile, median, third quartile, and maximum.
The five-number summary captures the center and spread of a distribution with five ordered values: minimum, (the first quartile), median, (the third quartile), and maximum. For example, the summary 2, 5, 8, 12, 20 says the data run from 2 to 20 with a median of 8. These five numbers are exactly what a boxplot draws, and the gap gives the interquartile range. Together they describe spread without assuming any particular distribution shape.
Quartile
Describing data
A quartile is one of three values that divide an ordered data set into four groups of roughly equal size.
Quartiles split ordered data into four parts, marked by the first quartile , the median, and the third quartile . The first quartile is the median of the lower half and the third quartile is the median of the upper half. For example, in 2, 4, 6, 8, 10 the median is 6, so you exclude it and get and . This site uses the median-excluded convention (the TI-84 method), which drops the overall median when the count is odd.