Quartile

A quartile is one of three values that cut an ordered dataset into four equal-sized quarters. Line your data up from smallest to largest, then find the points below which one quarter, one half, and three quarters of the values fall. Those cut points are the first quartile (Q1), the median or second quartile (Q2), and the third quartile (Q3). Q1 sits at the 25th percentile, the median at the 50th, and Q3 at the 75th. A quarter of the data lies below Q1, half lies below the median, and three quarters lie below Q3. Quartiles are order statistics — they care only about rank, not the exact spacing of values — which makes them robust to extreme outliers that would drag a mean around. That robustness is why they anchor the classic box plot.

The gap between the outer quartiles is where quartiles earn their keep. The interquartile range, or IQR, is Q3 minus Q1 — the span covering the middle half of the data. It is a resistant measure of spread. Because it ignores the top and bottom quarters, a few wild values cannot inflate it the way they inflate the standard deviation or the range. Analysts also use the quartiles to flag outliers, commonly tagging any point more than 1.5 times the IQR below Q1 or above Q3. Put the five numbers together — minimum, Q1, median, Q3, maximum — and you have the five-number summary, a compact portrait of a distribution's center, spread, and skew that fits on a single box-and-whisker plot.

Quartiles belong to a family of quantiles — cut points that split ranked data into equal-sized groups — and it helps to keep the relatives straight. A percentile divides the data into a hundred equal parts, so there are ninety-nine percentile cut points. The 25th percentile is exactly Q1, the 50th is the median, and the 75th is Q3. Quartiles are therefore just three specific percentiles given their own names. A quintile splits the data into five equal parts (four cut points), and a decile splits it into ten (nine cut points). The choice is about resolution. Percentiles give fine detail, quartiles give a quick four-way split, and quintiles a five-way one. Reach for quartiles when you want a simple, robust summary, and reach for percentiles when you need to pinpoint where a single value ranks.

The distinction matters most when people report a 'quartile' loosely. Sometimes 'top quartile' means the group of values above Q3 — the best-performing quarter — rather than the cut point Q3 itself. Both usages are common, so state which you mean. Percentiles avoid that ambiguity when you need precision. Saying a customer is at the 92nd percentile of spend is clearer than saying 'top quartile,' which only tells you they are in the upper quarter. Quintiles show up often in ranking and segmentation — dividing customers into five value tiers, for instance — because five buckets are granular enough to act on yet coarse enough to stay simple. Match the tool to the task. Quartiles for a fast robust overview, percentiles for exact standing, quintiles or deciles when four buckets are too few.

Use quartiles to summarize a distribution quickly and resist outliers. When a handful of huge orders or a few zero-value accounts would distort the mean, the median and the interquartile range describe the typical case far better. Build a box plot to show all three quartiles at once and let the shape reveal skew. A median sitting nearer Q1 than Q3 signals a right-skewed spread with a long high tail. Report the IQR alongside the median so readers see spread, not just center. And when you compare groups, setting their quartiles side by side often exposes differences that averages hide, because two datasets can share a mean yet have wildly different middle halves.

The failures are small but common. Be explicit about whether 'quartile' means a cut point or one of the four groups, or your audience will guess wrong. Watch out for the several accepted methods of computing quartiles on small samples, since different software can return slightly different Q1 and Q3, so note your method when the numbers matter. Do not reach for quartiles when the data is tiny, because a handful of points cannot support a meaningful four-way split. And remember that quartiles describe rank, not magnitude. They tell you where the middle half sits, not how far apart individual values are inside it. Paired with the median and the IQR, though, quartiles give a robust, honest summary that a single average rarely matches.

Quartile comes from the Latin quartus, meaning fourth, and entered statistics in the late nineteenth century alongside the median and percentile as English statisticians formalized the study of distributions.

Etymology: source.

Search interest for this term over the last five years:

View interest-over-time on Google Trends →

Areas of marketing where quartile is a core concern: