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Five Number Summary Calculator

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Five Number Summary Calculator

The five number summary is the minimum, first quartile, median, third quartile and maximum of a data set. Together they describe the centre, the spread of the middle half and the full range, and they are the five values a box-and-whisker plot is drawn from. Enter your data and the calculator sorts it, finds each of the five numbers and shows the work.

By default the quartiles use the median-of-halves rule that most introductory courses and the TI-84 use. Switch to linear interpolation if you need to match Excel’s QUARTILE.INC or Python, or to the exclusive method for Minitab. The IQR and range are reported alongside the summary.

A five number summary is the quickest way to compare two groups: put the summaries side by side, or draw them with the box plot maker, and you can see at a glance which group has the higher median and which has more spread.

Separate values with commas, spaces or new lines.

Result and step-by-step solution

MinimumQ1MedianQ3Maximum
37132125
  1. Sort the values (n = 11)
    3, 5, 7, 8, 12, 13, 14, 18, 21, 22, 25
  2. Minimum and maximum
    First and last sorted values: 3 and 25.
  3. Median
    Middle value (position 6): 13.
  4. Lower and upper quartiles
    Q1 is the median of the values below the median and Q3 the median of the values above it: Q1 = 7, Q3 = 21.
  5. Spread
    Range = 22; IQR = Q3 − Q1 = 14.

Frequently asked questions

What are the five numbers in a five number summary?
The minimum, the lower quartile (Q1), the median, the upper quartile (Q3) and the maximum, always listed in that order.
How is the five number summary used in a box plot?
The box runs from Q1 to Q3 with a line at the median. The whiskers extend to the minimum and maximum, or to the last values inside the 1.5 × IQR fences when outliers are drawn separately.
Is the median included in the halves when finding Q1 and Q3?
Under the Tukey rule used by default here, no: when n is odd the median is left out of both halves. Some textbooks include it; pick the linear method if yours does.
Can I use the five number summary to detect skew?
Yes. If the median sits closer to Q1 than to Q3, or the upper whisker is much longer than the lower one, the data is right-skewed; the reverse suggests left skew.

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Last reviewed: September 25, 2026. Calculations run in your browser and were validated against SciPy.

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