Five Number Summary Calculator

Compress any list of numbers into the five landmarks that describe its entire shape: minimum, first quartile, median, third quartile, and maximum. The tool adds the interquartile range and the full range as bonus measures, giving you everything needed to sketch a box plot or screen a new data set in seconds.

Why Five Numbers?

A single average says where data sits but nothing about how it stretches. The five-number summary fixes that with positions instead of formulas: the extremes bound the data, the quartiles bracket the middle half, and the median pins the center.

Because all five are order statistics — values read off the sorted list rather than computed from every point — the summary stays honest even when the data is skewed or contains extreme values.

Good Habits for Quick Screening

  • Run new data through this summary before any deeper analysis; impossible minimums or maximums expose data-entry errors immediately.
  • Compare the gap from Q1 to the median against the gap from the median to Q3 — unequal gaps are your first hint of skew.
  • Note the count alongside the five numbers; a summary of 8 values and one of 8,000 deserve different levels of trust.

Enter numbers separated by commas or spaces

From Five Numbers to a Box Plot

The five-number summary and the box plot are the same information in two formats — Tukey designed the plot as a direct picture of these five values. To draw one from this calculator's output: draw a number line covering the range, draw a box from Q1 to Q3, cut it with a line at the median, then extend whiskers out toward the minimum and maximum.

In the strict Tukey version, whiskers stop at the last data points inside the 1.5 × IQR fences and anything beyond is drawn as an individual dot. If you need those fences and a list of the flagged values, our quartile calculator computes them from the same quartiles you see here.

The Quartile Convention Used on This Page

Q1 and Q3 here come from the median-split (Moore & McCabe, exclusive) method: sort the data, locate the median, form a lower and an upper half — leaving the median itself out when the count is odd — and take the median of each half. It is the convention used across this site's quartile tools, so summaries here and fences on the quartile page always agree.

Interpolation-based conventions, such as the R-7 method behind Excel's QUARTILE.INC and our percentile calculator, can place Q1 and Q3 slightly differently on small data sets. When you report a five-number summary in coursework, name the method — on short lists the choice visibly changes the quartiles, and graders check.

Comparing Groups at a Glance

The summary's real power appears when you compute it for several groups side by side. Two classes might share an identical median exam score while one has a far wider box — same typical student, very different consistency. Sales regions, server response times before and after a deploy, or plant growth under two fertilizers all become comparable through five numbers each, no distributional assumptions required.

This positional approach complements rather than replaces moment-based summaries. The mean, median, mode calculator describes center through arithmetic and frequency, and the descriptive statistics calculator merges both views — quartiles alongside the mean — in one output when you want the complete inventory.

Worked Example: Ten Exam Scores

A teacher enters ten exam scores: 71, 58, 96, 65, 83, 52, 74, 61, 79, 68. The calculator works as follows:

  1. Sort: 52, 58, 61, 65, 68, 71, 74, 79, 83, 96 — so the minimum is 52 and the maximum is 96.
  2. Median: with an even count of 10, average the 5th and 6th values: (68 + 71) ÷ 2 = 69.5.
  3. Split into halves: lower half 52, 58, 61, 65, 68 and upper half 71, 74, 79, 83, 96 (an even count splits cleanly, nothing is excluded).
  4. Q1: median of the lower half — the 3rd of its 5 values — is 61.
  5. Q3: median of the upper half is 79.
  6. Bonus measures: IQR = 79 − 61 = 18; range = 96 − 52 = 44.

Reading the summary 52 | 61 | 69.5 | 79 | 96: the middle half of the class scored between 61 and 79, and the median student earned 69.5. The mean of these scores is 70.7 — barely above the median — so the distribution is close to balanced, with the strong 96 stretching the upper whisker slightly. One line of five numbers tells the whole story of the exam.

Frequently Asked Questions

What is a five-number summary used for?

It is the standard quick description of a distribution: the extremes show the full extent of the data, the quartiles show where the middle half lives, and the median marks the center. It is also the exact recipe for a box plot and a common first screening step before deeper statistical analysis.

How do I draw a box plot from these results?

Draw a scale covering the minimum to the maximum, draw a box from Q1 to Q3, mark the median with a line inside the box, and extend whiskers from the box toward the extremes. In Tukey's convention the whiskers stop at the last values within 1.5 x IQR of the box, and more extreme points are plotted individually as outliers.

Why does another calculator give me different quartiles?

Quartile conventions differ. This page uses the median-split method, which takes medians of the lower and upper halves of the data. Spreadsheets typically interpolate ranks across the whole data set instead. On small data sets the two approaches can disagree by a fraction of the gap between neighboring values; both are accepted, so state which one you used.

When should I report a five-number summary instead of mean and standard deviation?

Prefer the five-number summary when data is skewed, contains outliers, or is ordinal - cases where the mean and standard deviation mislead. Mean and standard deviation remain the better pair for roughly symmetric data feeding into methods that assume normality, such as t-tests or control charts.

Does the summary itself detect outliers?

Not directly - it reports the five landmark values, and the true minimum and maximum are always included among them. To flag outliers you extend the summary with Tukey fences at Q1 - 1.5 x IQR and Q3 + 1.5 x IQR, which is exactly what our quartile calculator does with the same quartile definitions.