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Box Plot Calculator

Build a box and whisker plot from your data. Five number summary, Q1, Q3, IQR, mean, and outliers using the 1.5 x IQR rule.

Box and whisker plot

n = 15

8.9514.72520.526.27532.05Q1 13.5Med 16Q3 18.5
BoxSpans Q1 to Q3 (interquartile range).
Median lineThe middle (50th percentile) value.
Mean markerThe arithmetic average, shown as a diamond.
Mild outlierBetween the inner and outer fences.
Extreme outlierBeyond the outer fences (3 x IQR rule).
WhiskersReach to the most extreme non-outlier value.

Five number summary

Min

10

Q1

13.5

Median

16

Q3

18.5

Max

31

IQR = 18.5 - 13.5 = 5. Range = 21.

Count (n)

15

Sum

255

Mean

17

Minimum

10

Q1 (25th percentile)

13.5

Median (Q2)

16

Q3 (75th percentile)

18.5

Maximum

31

IQR (Q3 - Q1)

5

Range (max - min)

21

Lower inner fence

6

Upper inner fence

26

Lower whisker end

10

Upper whisker end

22

Outliers (1.5 x IQR rule)

27, 31

Outlier analysis

The Tukey 1.5 x IQR rule classifies any value beyond the inner fences as a mild outlier. Values beyond the outer fences (3 x IQR) are typically called extreme outliers.

Mild outliers

27, 31

Extreme outliers

(none)

Step by step calculation

  1. Step 1: Sort the data set in ascending order10, 11, 12, 13, 14, 14, 15, 16, 16, 17, 18, 19, 22, 27, 31
  2. Step 2: Pick the median, Q1, and Q3Using the Inclusive (Excel INC, R type 7) method.Q1 = 13.5, Median = 16, Q3 = 18.5
  3. Step 3: Compute the interquartile rangeIQR = Q3 - Q1 = 18.5 - 13.5 = 5
  4. Step 4: Build the inner fences (1.5 x IQR)Lower = Q1 - 1.5 x IQR = 6Upper = Q3 + 1.5 x IQR = 26
  5. Step 5: Find the whisker ends and outliersLower whisker = 10 (smallest value within the inner fences)Upper whisker = 22 (largest value within the inner fences)Outliers: 27, 31

How to use

  1. Paste or type your numbers into the data set field. Separate values with commas, spaces, semicolons, or newlines. Decimals and negative numbers are supported.
  2. Pick a quartile method. Inclusive (R type 7 and NumPy default) matches most modern stats software. Exclusive matches Excel QUARTILE.EXC. Tukey hinges matches the classic textbook approach.
  3. Read the five number summary at the top and inspect the SVG box and whisker plot to see how the distribution is shaped.
  4. Check the outlier panel for mild outliers (between the inner and outer fences) and extreme outliers (beyond the outer fences).
  5. Use the step by step calculation block to see exactly how Q1, Q3, IQR, the fences, and the whisker ends were derived, then click Copy summary to share the result as plain text.

About this tool

Box Plot Calculator turns a raw list of numbers into a full five number summary and a real box and whisker plot. Paste or type your values separated by commas, spaces, or newlines and the tool sorts them, finds the minimum and maximum, computes the first quartile (Q1, the 25th percentile), the median (Q2, the 50th percentile), and the third quartile (Q3, the 75th percentile), then derives the interquartile range as IQR = Q3 - Q1. Three quartile methods are available so the result matches whatever software or textbook you are working from: the inclusive method (R type 7 and NumPy default) is the most common modern convention and uses linear interpolation between sorted ranks; the exclusive method matches Excel's QUARTILE.EXC by excluding the median from the half splits; and the Tukey hinges method is the classic textbook approach that takes the median of the lower half and the median of the upper half. The 1.5 x IQR rule classifies any value below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR as a mild outlier, while values beyond 3 x IQR from the box are flagged as extreme outliers in a separate group. The whiskers stretch to the smallest and largest values inside the inner fences, exactly as a standard Tukey box plot is drawn. An SVG diagram renders the box, the whiskers, the median line, the mean as a small diamond, and any outliers as labelled dots so you can see the shape of the distribution at a glance. A step by step walkthrough explains how each value was derived, which is useful for homework, take-home stats assignments, and quick sanity checks against R, Python, or Excel. Everything runs locally in the browser; the numbers you enter are never uploaded.

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