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Concept
Quartile
Summary
In statistics, a quartile is a type of quantile which divides the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic. The three main quartiles are as follows:
The first quartile (Q1) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower quartile, as 25% of the data is below this point.
The second quartile (Q2) is the median of a data set; thus 50% of the data lies below this point.
The third quartile (Q3) is the middle value between the median and the highest value (maximum) of the data set. It is known as the upper quartile, as 75% of the data lies below this point.
Along with the minimum and maximum of the data (which are also quartiles), the three quartiles described above provide a five-number summary of the data. This summary is important in statistics because it provides information about both the center and the spread of the data. Knowing the lower and upper quartile provides information on how big the spread is and if the dataset is skewed toward one side. Since quartiles divide the number of data points evenly, the range is not the same between quartiles (i.e., Q3-Q2 ≠ Q2-Q1) and is instead known as the interquartile range (IQR). While the maximum and minimum also show the spread of the data, the upper and lower quartiles can provide more detailed information on the location of specific data points, the presence of outliers in the data, and the difference in spread between the middle 50% of the data and the outer data points.
For discrete distributions, there is no universal agreement on selecting the quartile values.
Use the median to divide the ordered data set into two-halves.
If there is an odd number of data points in the original ordered data set, do not include the median (the central value in the ordered list) in either half.
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