Quartile
A quartile is one of three values that divide an ordered dataset into four equal-sized parts, each containing roughly a quarter of the observations. The first quartile (Q1) is the value below which 25% of the data falls — equivalent to the 25th percentile. The second quartile (Q2) is the median, the 50th percentile, splitting the data exactly in half. The third quartile (Q3) is the 75th percentile, the value below which 75% of the data falls. Quartiles are simply percentiles at these three specific, evenly-spaced positions, chosen for the convenience of a round, easily communicated four-way split rather than representing anything mathematically distinct from percentiles more generally.
Quartiles are the core building blocks of the five-number summary (minimum, Q1, median, Q3, maximum), the standard compact way to describe a distribution's center and spread without requiring a full histogram, and they are, directly, what's visualized in a box plot — a box drawn from Q1 to Q3 (capturing the middle 50% of the data, called the interquartile range), with a line marking the median inside it, and whiskers extending out toward the minimum and maximum (or toward a defined outlier threshold). This makes the box plot a particularly efficient visualization for comparing the spread and skew of several groups side by side at a glance — several box plots placed next to each other let a viewer compare medians, spreads, and the presence of outliers across groups far more quickly than scanning several separate sets of raw summary numbers would allow.
The difference between Q3 and Q1 — the interquartile range (IQR) — captures the spread of the middle 50% of a dataset specifically, deliberately excluding the most extreme 25% on either end, which makes it considerably more resistant to outliers than the full range (maximum minus minimum), since a single extreme value anywhere beyond Q1 or Q3 has no effect at all on where the quartiles themselves fall. This outlier resistance is exactly why the IQR is used in the standard statistical convention for flagging outliers: any value falling more than 1.5 times the IQR below Q1 or above Q3 is conventionally flagged as a potential outlier, a threshold formalized by statistician John Tukey (the same figure behind exploratory data analysis more broadly) and visually represented by a box plot's whiskers, which typically extend only to the most extreme non-outlier value rather than all the way to the dataset's absolute minimum and maximum.
There's more than one mathematically valid method for calculating quartiles on a given dataset — different statistical software packages (R's default method, Excel's, and several others) can produce slightly different quartile values for the exact same data, particularly for small sample sizes, because they handle the interpolation between data points differently when a quartile position doesn't land exactly on an existing observed value. This isn't usually a practically significant source of disagreement for large datasets, where the different methods converge to nearly identical results, but it's worth knowing about specifically because it means quartile and IQR values computed in two different tools aren't always bit-for-bit comparable, even when both are technically correct implementations.
Read a quartile as one of three evenly spaced percentile landmarks that together summarize a distribution's center and spread compactly: the interquartile range they define is a deliberately outlier-resistant measure of spread, the standard IQR-based outlier flagging rule (1.5 times the IQR beyond Q1 or Q3) is the most widely used formal convention for identifying potential outliers, and the box plot is simply this same set of values — five numbers, not a hundred — rendered visually, which is why it remains one of the fastest ways to compare the shape of several distributions side by side.