Are quartiles and percentiles different concepts?

Quartiles are specific percentiles: 25th, 50th and 75th for the three main cut points.

Is Q2 always the median?

Yes, Q2 refers to the 50th percentile or median, with the finite-sample calculation convention made explicit when needed.

Does being in the top quartile mean being above a fixed standard?

No. It is a relative position in a specified distribution. The threshold depends on the reference data and grouping rules.

AI Glossary / Data science and analytics / Beginner

Quartile

Definition

A quartile is a cut point in an ordered distribution associated with quarters of its cumulative probability. The first quartile, Q1, is the 25th percentile; Q2 is the median; and Q3 is the 75th percentile. Sample quartile calculations depend on the chosen convention.

What it means

Quartiles describe where values sit in an ordered dataset. They help summarize the center and spread without relying only on the mean or the most extreme observations.

The difference Q3 − Q1 is the interquartile range, or IQR. It describes the span between the lower and upper quartile cut points and is commonly used to summarize the central part of a distribution. A box plot usually uses those cut points to form its box.

The term can also refer informally to one of four groups, such as the “top quartile” of scores. Distinguish a cut-point value from membership in a group. Ties and small samples mean that a simple cut at a quartile value does not always put exactly one quarter of the observations into each group.

How it works

Order the observations from smallest to largest, then use a stated rule to estimate the 25th, 50th and 75th percentiles. Some rules use selected ordered values; others interpolate between them.

A common classroom procedure finds the median and then takes the medians of the lower and upper halves. For an odd number of observations, whether the overall median is included in those halves changes the result. Software also offers percentile methods that do not follow that classroom procedure.

For large, smooth datasets, different reasonable methods often give similar answers. In small or heavily tied datasets, differences can matter. Record the method when results need to be reproduced, compared or used as decision thresholds.

Quartiles retain the measurement units of the data. If response times are measured in minutes, Q1, Q2, Q3 and the IQR are also measured in minutes; they are not percentages of the measured quantity.

Three practical examples

A service team reports the median and interquartile range of waiting times to describe typical experience and variation.
An analyst compares box plots across branches to see whether differences concern the middle, spread or extreme values.
An AI evaluation team examines score quartiles to see whether an average result hides a weaker lower portion of the evaluation cases.

Think of it this way

Think of placing markers along a queue ordered by a measured value. The markers describe positions in the ordered group, not equal-sized gaps on the measurement scale.

The analogy has limits because sample quantiles may fall between observed values and ties may span a marker. Quartiles divide probability or ranked position conceptually; they do not require the numerical distance between neighboring markers to be equal.

Worked example

Take the invented ordered values 2, 4, 6, 8, 10, 12 and 14. The median is 8. Using the convention that excludes this overall median from the two halves, the lower half is 2, 4, 6 and the upper half is 10, 12, 14.

Their medians give Q1 = 4 and Q3 = 12, so the IQR is 12 − 4 = 8.

Now use a common linear-interpolation percentile rule with position 1 + (n − 1)p. For n = 7 and p = 0.25, the position is 2.5, halfway between 4 and 6, giving Q1 = 5. At p = 0.75, position 5.5 gives Q3 = 11. This method gives IQR = 6.

Neither difference is an arithmetic accident: the rules differ. A report that uses quartiles as thresholds should state which rule it uses, especially when a small dataset places cases near a boundary.

Illustrative case study

Illustrative fictional case: Northwood Support compares a spreadsheet report with a Python analysis and finds different upper quartiles for the same small set of response times. The team first suspects that one file has missing records.

After checking the data, the analyst identifies different percentile conventions. The team chooses and documents a common method for the shared report and retains the distinction between a descriptive quartile and a service commitment.

It also reviews tied values before labeling exactly 25% of cases as the “slowest quartile.” The fictional lesson is that matching data does not guarantee matching summaries unless the calculation and grouping rules are aligned.

Common misconceptions and mistakes

Do not calculate quartiles by dividing the numerical range into four equal widths. That creates equal-width intervals, not quartile cut points.

Do not assume every software package uses the same sample definition. Avoid claiming that all observations between Q1 and Q3 constitute exactly 50% under every finite-sample and tie convention. A quartile is not a quality target, confidence bound or probability that a future observation will fall in a particular range without further assumptions.

Business use

Quartiles can make operational summaries more informative when averages alone hide uneven experience. Pair them with sample size, period and a clear definition of the measured quantity.

When quartiles drive segmentation or performance labels, specify the reference population, calculation method and tie handling. Recomputing cut points in each period can change category membership even if an individual's absolute value stays unchanged. AI-generated commentary should distinguish a relative ranking from an absolute improvement or deterioration in the underlying measure.

Check your understanding

A team splits values from 0 to 100 into intervals 0-25, 25-50, 50-75 and 75-100. Has it necessarily calculated quartile groups?

Answer: No. Those are equal-width value intervals. Quartile boundaries depend on the distribution of observations, not just the minimum and maximum.

Related terms

Learn next

Read percentile and interquartile range. Calculate quartiles for a small ordered dataset using two stated conventions and compare the results. Then add tied observations and explain how a value threshold differs from an exactly equal-sized group assignment.

Percentile

Sources

NIST, percentile definitions and calculation methods: https://itl.nist.gov/div898/handbook/prc/section2/prc262.htm

NIST, quartiles and box plots: https://www.itl.nist.gov/div898/handbook/eda/section3/boxplot.htm

Eric Langford, Quartiles in Elementary Statistics: https://jse.amstat.org/v14n3/langford.html

The seven-value calculation and support-report case are original fictional illustrations.

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