Knowra Quartile Quartile A quartile is one of four groups formed by dividing ordered data into equal parts, or one of the three values marking those divisions. Conventions differ when locating quartiles in finite samples.
Median : The middle value of ordered data, or the average of the two middle values when the count is even. The second quartile is the median, and the other quartiles divide data around it.
Tukey hinges : Quartile estimates obtained by finding the medians of the lower and upper halves of ordered data. This convention gives quartiles by splitting the sample around its median.
Box plot : A graph that displays a distribution using quartiles, a median, and whiskers for its spread. The box spans the first and third quartiles, with the median marked inside.
Arithmetic mean : The sum of numerical observations divided by their count. Unlike quartiles, the mean incorporates every value and shifts strongly with extreme observations.
Percentile : A value on a scale from 0 to 100 that indicates the percentage of observations at or below it. Quartiles are the 25th, 50th, and 75th percentile markers under common conventions.
Linear interpolation : A method for estimating a value between two known points by taking a weighted average. Some sample-quantile rules interpolate between adjacent ordered observations.
Interquartile range rule : A rule that flags observations below Q1 − 1.5 IQR or above Q3 + 1.5 IQR as potential outliers. It uses quartiles to identify unusually distant observations without assuming a normal distribution.
Range (statistics) : The difference between the largest and smallest observations in a dataset. The range depends only on extremes, whereas the interquartile range tracks the middle half.
Order statistic : A value selected by its position in a sample sorted from smallest to largest. Sample quartiles are computed from ordered positions, with methods differing on interpolation.
Hyndman–Fan quantile definitions : A classification of nine algorithms for estimating sample quantiles from ordered observations. It documents why software packages may report different quartiles for identical data.
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