Box Plot Calculator

Enter your data and instantly generate a box plot with the five-number summary: minimum, Q1, median, Q3, maximum, and outliers detected by the 1.5×IQR rule.

What is a Box Plot?

A box plot (box-and-whisker plot) is a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

The box spans the interquartile range (IQR = Q3 − Q1), which contains the middle 50% of the data. The whiskers extend to the most extreme values that are not outliers, and individual outliers are plotted as separate points.

Box plots make it easy to compare distributions, spot skewness (when the median is off-center within the box) and identify unusual values at a glance.

How to Use This Calculator

Follow these steps:

  1. Paste or type your numeric data separated by commas, spaces or newlines.
  2. The five-number summary and mean are computed instantly, and the box plot is drawn automatically.
  3. Outliers detected by the 1.5 × IQR rule are listed and marked on the plot. Share the URL to send the exact dataset to someone else.

Worked Example

For the data 3, 7, 8, 5, 12, 14, 21, 13, 18:

Sorted: 3, 5, 7, 8, 12, 13, 14, 18, 21 Median (Q2) = 12 Q1 = 7, Q3 = 14, IQR = 7 Lower fence = 7 − 10.5 = −3.5, upper fence = 14 + 10.5 = 24.5 No outliers: all values lie within the fences.

Frequently Asked Questions

Have another question? Let us know.

What is the interquartile range (IQR)?

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). It measures the spread of the middle 50% of the data and is robust to outliers.

How are outliers detected in a box plot?

Using the 1.5 × IQR rule: a value is an outlier if it is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. These values are plotted as individual points beyond the whiskers.

What does a box plot tell me about skewness?

If the median is closer to Q1, the distribution is right-skewed; if closer to Q3, left-skewed. Longer whiskers on one side also indicate skew in that direction.

Can I compare two datasets with box plots?

Yes. Placing box plots side by side lets you compare medians, spreads (box and whisker lengths) and outlier patterns across groups quickly.

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