Quartile
Quartiles divide a data series into four quarters. A quartile is accordingly the border between two specific quarters. The median halves the data series. The first and third quartiles divide the two halves again.
There are always three quartiles:
- The 1st quartile (also called lower quartile) divides the first quarter and the second quarter.
- The 2nd quartile always corresponds to the median. He divides the second and third quarters.
- The 3rd quartile (also called upper quartile) divides the third and fourth / last quarters.
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Method
- Sort data set in ascending order by size
- Determine median (2nd quartile)
- Determine medians of the 2 halves (1st and 3rd quartile)
Example
-
Sort the data series by size:
$8, 8, 12, 13, 14, 18, 23$ -
Determine median:
$8, 8, 12, \color{red}{\textbf{13}}, 14, 18, 23$
The median or 2nd quartile is $\color{red}{13}$ -
Determine medians of the halves
$8, \color{blue}{\textbf8}, 12, \color{red}{13}, 14, \color{green}{\textbf{18}}, 23$
The median of the first half or the 1st quartile is $\color{blue}{8}$
The median of the second half or the 3rd quartile is $\color{green}{18}$