Quartiles
Quartiles[list]
gives a list of the 1/4, 1/2 and 3/4 quantiles of the elements in list.
Quartiles[dist]
gives a list of the 1/4, 1/2 and 3/4 quantiles of the distribution dist.
Details

- Quartiles[list] is equivalent to Quantile[list,{1/4,1/2,3/4},{{1/2,0},{0,1}}]. »
- The second quartile is equivalent to Median[list]. »
- For even Length[list], the first quartile is equivalent to the median of the
smallest elements in list.
- For odd Length[list], the first quartile is equivalent to the average of the median of the
smallest elements and the median of the
smallest elements in list.
- The third quartile is defined like the first, but with the largest rather than smallest elements.
- Quartiles[list,{{a,b},{c,d}}] uses the quantile definition specified by parameters a, b, c, d.
Examples
open allclose allScope (14)
Data (11)
Exact input yields exact output:
Approximate input yields approximate output:
Quartiles for a matrix gives columnwise quartiles:
SparseArray data can be used just like dense arrays:
Compute results using other parametrizations:
Find the quartiles of WeightedData:
Find the quartiles of EventData:
Find the quartiles of TemporalData:
Find the quartiles of TimeSeries:
Applications (4)
Quartiles divide a distribution in four equal probability sections:
Find a moving quartile envelope for a time series:
Data smoothed by moving median:
Moving envelope of first and third quartiles:
Find the quartiles for data representing the top oil-producing fields in 2001:
Compare with the minimum and maximum values for the data:
Plot the data with quartile lines:
Compute the quartiles for the heights of children in a class:
Properties & Relations (6)
Quartiles are given by linearly interpolated Quantile values:
The second quartile is the Median:
InterquartileRange is the difference between the first and third quartiles:
QuartileDeviation is half the difference between the first and third quartiles:
QuartileSkewness is a skewness measure obtained from the quartiles:
BoxWhiskerChart shows the quartiles for data:
Possible Issues (1)
Quartiles requires numeric values:

Text
Wolfram Research (2007), Quartiles, Wolfram Language function, https://reference.wolfram.com/language/ref/Quartiles.html (updated 2017).
CMS
Wolfram Language. 2007. "Quartiles." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Quartiles.html.
APA
Wolfram Language. (2007). Quartiles. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Quartiles.html