# Five Number Summary Calculator URL: https://speedycalculator.com/calculators/statistics/5-number-summary/ Last updated: 2026-10-30 > The five number summary calculator finds the minimum, first quartile, median, third quartile and maximum of a data set, plus the range, the interquartile range, outlier fences and a box plot. Choose the quartile method your course or software uses. ## Inputs - Data set - Quartile method ## Results - Five-number summary (min, Q1, median, Q3, max) - Minimum - First quartile (Q1) - Median (Q2) - Third quartile (Q3) - Maximum - Range (max − min) - Interquartile range (IQR = Q3 − Q1) - Lower fence (Q1 − k × IQR) - Upper fence (Q3 + k × IQR) - Outliers - Number of values - Box plot - Sorted data - Step-by-step working ## Formula ``` Five-number summary = (min, Q1, median, Q3, max) · IQR = Q3 − Q1 · range = max − min ``` ## Explanation The five-number summary condenses a data set into five values that mark its edges and its quarters. The minimum and maximum show the full extent of the data, the median splits it in half, and the first and third quartiles enclose the middle 50%. Between any two neighbouring numbers of the summary lie about a quarter of the observations. Because it uses positions in the sorted data rather than the mean, the summary is resistant to extreme values and works for skewed data such as incomes, reaction times or house prices. It is the basis of the box-and-whisker plot, and comparing the gaps (median − Q1 versus Q3 − median, or the two whisker lengths) reveals skewness at a glance. Quartiles can be computed in several ways. The default here is the textbook rule – the median of the lower and upper halves, leaving out the overall median when n is odd – and you can switch to the Excel or Minitab definitions. The step-by-step box shows which values went into each quartile. ### How to use the Five Number Summary Calculator - **Data set** - **Quartile method** Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server. ### How it works Sort the data. The minimum and maximum are the first and last values; the median is the middle value (or the mean of the two middle values). Q1 and Q3 are found with the chosen quartile method, and the fences at 1.5 × IQR beyond the box flag any outliers on the box plot. ### Worked example Thirteen quiz scores: 12, 15, 18, 21, 22, 25, 27, 30, 31, 34, 38, 41, 45 (already sorted). The minimum is 12 and the maximum is 45. With n = 13 the median is the 7th value, 27. The lower half without the median is 12, 15, 18, 21, 22, 25, whose median is (18 + 21)/2 = 19.5 = Q1; the upper half 30, 31, 34, 38, 41, 45 gives Q3 = (34 + 38)/2 = 36. Five-number summary: **12, 19.5, 27, 36, 45**. IQR = 16.5, range = 33, and the fences −5.25 and 60.75 show there are no outliers. ### How to read the summary Each of the four gaps holds about 25% of the data. In the example the gaps are 7.5 (min to Q1), 7.5 (Q1 to median), 9 (median to Q3) and 9 (Q3 to max): the upper half is a little more spread out, a mild right skew. If one gap is several times longer than the others, look at that tail for outliers or a long tail. ### Quartile methods compared Statistics packages do not agree on one definition of a quartile. For the 10 values 68, 72, 75, 79, 81, 84, 86, 90, 93, 97 the four methods offered here give: MethodUsed byQ1Q3IQRMedian of halves (median excluded)TI-84, most school textbooks759015Linear interpolation, position 1 + (n − 1)pExcel QUARTILE.INC, R type 7, Google Sheets768913(n + 1)p positionsExcel QUARTILE.EXC, Minitab74.2590.7516.5Median of halves (median included)Tukey's hinges759015With an even number of values the two "halves" methods coincide; they differ only when n is odd. The differences shrink as the data set grows, so with a few hundred values the choice rarely matters. ## Worked example Inputs — Data set: 12, 15, 18, 21, 22, 25, 27, 30, 31, 34, 38, 41, 45; Quartile method: Median of halves, median excluded (TI-84, most textbooks). Results — **Five-number summary (min, Q1, median, Q3, max) = 12, 19.5, 27, 36, 45**; Minimum = 12; First quartile (Q1) = 19.5; Median (Q2) = 27; Third quartile (Q3) = 36; Maximum = 45. ## Key terms - **Quartile**: A value that cuts off a quarter (Q1) or three quarters (Q3) of the sorted data. - **Median**: The middle value of the sorted data (Q2). - **Interquartile range**: Q3 − Q1, the spread of the middle half of the data. - **Box plot**: A chart drawn from the five-number summary. ## FAQ **What is the five-number summary?** Minimum, first quartile (Q1), median, third quartile (Q3) and maximum, in that order. **How do I find the five-number summary?** Sort the data, take the smallest and largest values, find the median, then find the median of each half for Q1 and Q3. **What is the five-number summary of 12, 15, 18, 21, 22, 25, 27, 30, 31, 34, 38, 41, 45?** 12, 19.5, 27, 36, 45 with the textbook method (halves without the median). **Why does my calculator give different quartiles?** Different tools use different quartile definitions. Excel's QUARTILE.INC would give Q1 = 21 and Q3 = 34 for the example data. Pick the matching method in the menu. **How is the five-number summary related to a box plot?** The box runs from Q1 to Q3 with a line at the median; the whiskers reach towards the minimum and maximum (stopping at the fences if there are outliers). **Can I use the five-number summary for skewed data?** Yes – it is the preferred summary for skewed data because quartiles are not pulled by extreme values. **How many values do I need?** At least three; with fewer than about eight values each quartile rests on only one or two observations. ## Sources - [NIST/SEMATECH e-Handbook – Box plot](https://www.itl.nist.gov/div898/handbook/eda/section3/boxplot.htm) - [OpenStax – Introductory Statistics 2e](https://openstax.org/details/books/introductory-statistics-2e) - [Wolfram MathWorld – Quartile](https://mathworld.wolfram.com/Quartile.html)