Free chart tool

Free Box Plot Maker

A box plot is a chart that shows a dataset's five-number summary: the minimum, first quartile, median, third quartile, and maximum, with outliers plotted as separate points. Paste numbers or upload a CSV below to get a box and whisker plot, the five-number summary worked out step by step, and side-by-side group comparisons, free and without signing up.

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Step 1

Add your data

Examples (illustrative sample data)

Data source

17 values read.

16 values read.

15 values read.

3 of 8 groups

Separate numbers with commas, spaces, tabs, semicolons, or new lines, or paste a spreadsheet column. Negatives, decimals, and scientific notation such as 2.5e3 work. Up to 50,000 values in total.

Up to 5 MB. The file is read in your browser and never uploaded.

Or paste a table from a spreadsheet

48 values read in 3 groups.

Step 2

Choose the method and view

Exclusive leaves the median out of both halves when n is odd; inclusive keeps it in both; linear interpolation matches Excel and R. The median never changes, but Q1, Q3, and outliers can differ slightly between calculators.

Whiskers

Tukey whiskers end at the last value inside Q1 - k x IQR and Q3 + k x IQR; points beyond are outliers. Use 3 x IQR to flag only extreme outliers.

Orientation

Step 3

Your box plot

Support first-response time by plan (illustrative data)Box plot of Hours to first response comparing 3 groups. Free (n = 17): median 22, Q1 15.25, Q3 31.5, range 6.5 to 72, 1 outlier; Pro (n = 16): median 7.5, Q1 4.75, Q3 10.5, range 2.5 to 31, 1 outlier; Enterprise (n = 15): median 2, Q1 1.2, Q3 3, range 0.5 to 9.5, 1 outlier.Support first-response time by plan (illustrative data)020406080Freen = 17Pron = 16Enterprisen = 15Hours to first response
Box plot data: five-number summary per group
GroupnMinQ1MedianQ3MaxOutliers
Free176.515.252231.57272
Pro162.54.757.510.53131
Enterprise150.51.2239.59.5

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Five-number summary and outliers

Summary statistics per group
GroupnMinQ1MedianQ3MaxIQRMeanSDFencesOutliers
Free176.515.252231.57216.2525.17615.3-9.125 to 55.8751: 72
Pro162.54.757.510.5315.758.9066.763-3.875 to 19.1251: 31
Enterprise150.51.2239.51.82.522.175-1.5 to 5.71: 9.5

Quartiles use the exclusive median of halves (ti-84, most textbooks) method. SD is the sample standard deviation (n - 1). Fences are Q1 - 1.5 x IQR and Q3 + 1.5 x IQR.

Five-number summary, step by step

How the median, quartiles, IQR, and fences were found with the method you chose.

  1. 1.Sort the data

    17 values in order: 6.5, 9, 12, 14.5, 16, 18, 19.5, 21, 22, 24, 26, 27.5, 30, 33, 36, 41, 72.

  2. 2.Find the median

    n = 17 is odd, so the median is the middle value, number 9: 22.

  3. 3.Find Q1 and Q3

    n is odd, so the median is left out of both halves (exclusive method). Lower half (8 values): 6.5, 9, 12, 14.5, 16, 18, 19.5, 21; its median is Q1 = 15.25. Upper half (8 values): 24, 26, 27.5, 30, 33, 36, 41, 72; its median is Q3 = 31.5.

  4. 4.Compute the IQR

    IQR = Q3 - Q1 = 31.5 - 15.25 = 16.25.

  5. 5.Compute the fences

    Lower fence = Q1 - 1.5 x IQR = 15.25 - 1.5 x 16.25 = -9.125. Upper fence = Q3 + 1.5 x IQR = 31.5 + 1.5 x 16.25 = 55.875.

  6. 6.Draw the whiskers and outliers

    Whiskers reach the most extreme values inside the fences: 6.5 and 41. 1 value outside the fences is an outlier: 72.

  7. 7.Five-number summary

    Min 6.5, Q1 15.25, median 22, Q3 31.5, max 72.

How to make a box plot

  1. Step 1

    Order the data

    Sort the values from smallest to largest. The first value is the minimum and the last is the maximum.

  2. Step 2

    Find the median

    The median is the middle value when n is odd, or the average of the two middle values when n is even.

  3. Step 3

    Find Q1 and Q3

    Q1 is the median of the lower half of the data and Q3 is the median of the upper half. With the exclusive method, the median is left out of both halves when n is odd.

  4. Step 4

    Compute the IQR and fences

    The interquartile range is IQR = Q3 - Q1. The fences are Q1 - 1.5 x IQR and Q3 + 1.5 x IQR.

  5. Step 5

    Draw the box and whiskers

    Draw a box from Q1 to Q3 with a line at the median. Extend each whisker to the most extreme data point that is still inside the fences.

  6. Step 6

    Plot the outliers

    Mark every value outside the fences as an individual point beyond the whiskers.

How to read a box plot

  • The line in the box is the median. Half of the values are below it and half above. Compare medians across boxes to see which group is typically higher.
  • The box holds the middle 50%. Its length is the IQR. A tall box means inconsistent results; a short box means values cluster tightly.
  • Whiskers show the typical range. A longer upper whisker, or a median close to the bottom of the box, points to right skew, common for response times and revenue.
  • Dots beyond the whiskers are outliers. Check them before you delete them: an unusually slow ticket or a power user is often the most interesting data point. To see the full shape, use the histogram maker.

Quartile methods at a glance

Results for the data 1, 2, 3, 4, 5, 6, 7, 8, 9 (median 5). The methods agree on the median but can disagree on Q1 and Q3, so your IQR and outliers may differ slightly from another calculator.

Quartile methods, an example result, and where each is used
Method1 to 9Used by
Exclusive median of halvesQ1 = 2.5, Q3 = 7.5Default. TI-84 calculators and most statistics textbooks.
Inclusive median of halvesQ1 = 3, Q3 = 7Tukey's hinges, used in some textbooks and exploratory data analysis.
Linear interpolation (type 7)Q1 = 3, Q3 = 7Excel QUARTILE.INC, Google Sheets QUARTILE, R quantile() default, NumPy default.

Using box plots for product feedback

Response times by plan

One box per plan shows whether paying customers really get faster replies, and the outlier dots point you to the tickets that waited far too long.

Scores by segment

Plot 0 to 10 ratings for each segment to compare medians and spread, then turn the same ratings into a score with the NPS calculator.

Before and after a release

Compare task times or usage before and after a change, then check whether the difference is real with the significance calculator.

Box plot questions

What is a box plot?

A box plot, or box and whisker plot, is a chart that shows a dataset's five-number summary: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box spans Q1 to Q3 with a line at the median, whiskers reach out to the most extreme values that are not outliers, and outliers are drawn as separate points.

What is the five-number summary?

The five-number summary is the minimum, first quartile (Q1, the 25th percentile), median (the 50th percentile), third quartile (Q3, the 75th percentile), and maximum of a dataset. Together they describe the center, the spread of the middle half (the IQR, Q3 - Q1), and the full range in five values.

How do you make a box and whisker plot?

Sort the data, find the median, then find Q1 as the median of the lower half and Q3 as the median of the upper half. Compute the IQR = Q3 - Q1 and the fences Q1 - 1.5 x IQR and Q3 + 1.5 x IQR. Draw a box from Q1 to Q3 with a line at the median, extend whiskers to the most extreme values inside the fences, and plot any values beyond the fences as individual points.

How are outliers found in a box plot?

Most box plots use Tukey's 1.5 x IQR rule: a value is an outlier if it is below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR. Values beyond 3 x IQR from the box are often called extreme outliers. This tool lets you switch between 1.5 and 3, or draw whiskers from the minimum to the maximum with no outliers.

Why do different calculators give different quartiles?

There is no single standard for quartiles. The TI-84 and most textbooks leave the median out of both halves when n is odd (the exclusive method); Tukey's hinges include it in both halves (the inclusive method); and Excel QUARTILE.INC, Google Sheets QUARTILE, and R's default interpolate between sorted values (type 7). The median is always the same, but Q1, Q3, the IQR, and therefore the outliers can differ slightly, especially for small samples. Pick the method your class or team uses.

Box plot vs histogram: which should I use?

Use a box plot to compare the center, spread, and outliers of several groups side by side in little space. Use a histogram to see the full shape of one distribution, such as two peaks or a long tail, which a box plot hides. Many analyses use both: a box plot to compare segments and a histogram to inspect each one.

Want the full picture of one distribution instead? Try the free histogram maker. For background on quartile definitions, see Quartile on Wikipedia.

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