# What does my box plot look like?

Draws a box plot of a list of numbers and gives its five-number summary, IQR, whisker ends and outliers, by the quartile method you choose.

- Page: https://www.acalculator.org/statistics/box-plot-calculator
- JSON spec: https://www.acalculator.org/statistics/box-plot-calculator.json
- Version: 2a7364ee3ba8

## Default answer

Example with the default inputs (Your numbers [1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5], Quartile method Median of halves (TI-83), Whiskers Min to max): The five-number summary of the 14 numbers is 1, 2, 7, 9, 11.5, and the IQR is 7.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| data | Your numbers | The numbers, separated by commas, spaces, semicolons, or new lines. |
| method | Quartile method | How Q1 and Q3 are found. The methods agree on the median but can differ on Q1 and Q3. |
| whiskers | Whiskers | Whiskers to the minimum and maximum, or to the last values inside the 1.5 × IQR fences. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| summary | Five-number summary | The minimum, Q1, median, Q3 and maximum, in that order. |
| min | Minimum | The smallest number in the list. |
| q1 | First quartile (Q1) | The 25th percentile by the chosen method. |
| median | Median | The middle value. |
| q3 | Third quartile (Q3) | The 75th percentile by the chosen method. |
| max | Maximum | The largest number in the list. |
| iqr | Interquartile range (IQR) | Q3 minus Q1: the width of the box. |
| lowWhisker | Lower whisker end | Where the lower whisker stops. |
| highWhisker | Upper whisker end | Where the upper whisker stops. |
| outliers | Outliers | Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR, smallest first, or None. |
| n | Count (n) | How many numbers are in the list. |

## Method

Sort the numbers; the median is the middle value; Q1 and Q3 follow the chosen method; the box runs from Q1 to Q3; the whiskers run to the minimum and maximum, or to the last values inside Q1 − 1.5 × IQR and Q3 + 1.5 × IQR.

## Assumptions

- The default method (median of halves, median left out) matches the quartile calculator and OpenStax.
- With one number, every value of the summary is that number.
- A value exactly on a fence is not an outlier.

## Worked examples

1. data = 1 or 1, method = moore-mccabe, whiskers = minmax gives summary = 1, 2, 7, 9, 11.5, q1 = 2, median = 7, q3 = 9, iqr = 7, lowWhisker = 1, highWhisker = 11.5, outliers = None. Source: OpenStax, Introductory Statistics 2e, §2.4 Box Plots (minimum, Q1, median, Q3, maximum; 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5 gives 1, 2, 7, 9, 11.5), https://openstax.org/books/introductory-statistics-2e/pages/2-4-box-plots (retrieved 2026-10-05).
2. data = 10 or 20, method = moore-mccabe, whiskers = fences gives summary = 10, 30, 55, 80, 1000, iqr = 50, lowWhisker = 10, highWhisker = 90, outliers = 1000. Source: NIST/SEMATECH e-Handbook of Statistical Methods, §7.1.6 What are outliers in the data? (fences Q1 − 1.5 IQ and Q3 + 1.5 IQ), https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm (retrieved 2026-10-05); OpenStax, Introductory Statistics 2e, §2.4 Box Plots (minimum, Q1, median, Q3, maximum; 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5 gives 1, 2, 7, 9, 11.5), https://openstax.org/books/introductory-statistics-2e/pages/2-4-box-plots (retrieved 2026-10-05).
3. data = 1 or 2, method = inclusive, whiskers = minmax gives summary = 1, 3.25, 5.5, 7.75, 10, iqr = 4.5. Source: OpenStax, Introductory Statistics 2e, §2.4 Box Plots (minimum, Q1, median, Q3, maximum; 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5 gives 1, 2, 7, 9, 11.5), https://openstax.org/books/introductory-statistics-2e/pages/2-4-box-plots (retrieved 2026-10-05).
4. data = 1 or 2, method = exclusive, whiskers = minmax gives summary = 1, 2.75, 5.5, 8.25, 10, iqr = 5.5. Source: OpenStax, Introductory Statistics 2e, §2.4 Box Plots (minimum, Q1, median, Q3, maximum; 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5 gives 1, 2, 7, 9, 11.5), https://openstax.org/books/introductory-statistics-2e/pages/2-4-box-plots (retrieved 2026-10-05).
5. data = 1 or 2, method = tukey, whiskers = minmax gives summary = 1, 3, 5, 7, 9, iqr = 4. Source: OpenStax, Introductory Statistics 2e, §2.4 Box Plots (minimum, Q1, median, Q3, maximum; 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5 gives 1, 2, 7, 9, 11.5), https://openstax.org/books/introductory-statistics-2e/pages/2-4-box-plots (retrieved 2026-10-05).

## FAQ

### What is a box plot?

A box plot, or box-and-whisker plot, draws the five-number summary of a data set. The box runs from the first quartile Q1 to the third quartile Q3, a line inside it marks the median, and whiskers reach out to the smallest and largest values. The middle half of the data falls inside the box.

### How do I make a box plot?

Sort the data. Find the minimum, Q1, the median, Q3 and the maximum. Draw a number line, a box from Q1 to Q3 with a line at the median, and whiskers from the box out to the minimum and maximum. For 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5 these are 1, 2, 7, 9 and 11.5.

### What are the whiskers in a box plot?

In the simplest box plot the whiskers reach the minimum and maximum. In a modified box plot they stop at the last values inside the fences Q1 − 1.5 × IQR and Q3 + 1.5 × IQR, and values beyond the fences show as separate dots (outliers). Pick either style with the Whiskers choice.

### How do I find outliers from a box plot?

Work out the IQR = Q3 − Q1. Any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is an outlier. For 10, 20, …, 90 and 1000, the IQR is 50 and the upper fence is 155, so 1000 is an outlier.

### Why does my box plot differ from another calculator's?

There are several standard ways to find Q1 and Q3, and they can differ for the same data. This page offers the median-of-halves method (TI-83 and many textbooks), Tukey's hinges, and the inclusive and exclusive methods of Excel. All give the same median.

### What does the shape of a box plot tell me?

A long box means the middle half of the data is spread out. If the median sits near one end of the box, or one whisker is much longer than the other, the data are skewed toward the long side.

## Sources

- OpenStax, Introductory Statistics 2e, §2.4 Box Plots: the five-number summary, the box from Q1 to Q3 holding the middle 50% of the data, and whiskers to the extreme values (or outliers as dots). https://openstax.org/books/introductory-statistics-2e/pages/2-4-box-plots (retrieved 2026-10-05)
- NIST/SEMATECH e-Handbook of Statistical Methods, §7.1.6 What are outliers in the data?: the fences Q1 − 1.5 × IQ and Q3 + 1.5 × IQ. https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm (retrieved 2026-10-05)
- NIST/SEMATECH e-Handbook of Statistical Methods, §7.2.6.2 Percentiles: sample quantiles by linear interpolation. https://www.itl.nist.gov/div898/handbook/prc/section2/prc262.htm (retrieved 2026-10-05)