Box Plot & Quartile Calculator

A box plot, or box-and-whisker plot, summarises data with five numbers: the minimum, lower quartile, median, upper quartile and maximum. This calculator sorts the data, finds the quartiles, works out the interquartile range, flags outliers with the 1.5 × IQR rule and draws the box plot.

Try:

How to use the box plot & quartile calculator

  1. Type or paste at least four data values.
  2. Press Calculate.
  3. Read the five-number summary, the IQR, any outliers and the box plot.

Formula

IQR=Q3−Q1\text{IQR} = Q_3 - Q_1

Worked example: 11 values with an outlier

  • Data values: 7, 15, 36, 39, 40, 41, 42, 43, 47, 49, 95

✓ Answer checked

Min=7,  Q1=36,  Median=41,  Q3=47,  Max=95\text{Min} = 7,\; Q_1 = 36,\; \text{Median} = 41,\; Q_3 = 47,\; \text{Max} = 95
Interquartile range (IQR)
1111
Outlier fences
19.5 and 63.519.5 \text{ and } 63.5
Outliers
7, 15, 95
Range
8888
0102030405060708090100min 36Q1 36median 41Q3 47max 49
The box spans the middle 50% of the data (IQR 11); the line inside is the median. Dots are outliers beyond 1.5 × IQR.
Step-by-step working (4 steps)

  1. Sort the data

    Order the 11 values.

    7,  15,  36,  39,  40,  41,  42,  43,  47,  49,  957,\; 15,\; 36,\; 39,\; 40,\; 41,\; 42,\; 43,\; 47,\; 49,\; 95

  2. Median

    The middle value splits the data into two halves.

    Q2=41Q_2 = 41

  3. Quartiles Quartiles (Tukey method)

    Q1 is the median of the lower half and Q3 of the upper half (the overall median is left out of both halves).

    Q1=36,Q3=47Q_1 = 36,\quad Q_3 = 47

  4. IQR and outliers 1.5 × IQR rule

    Values more than 1.5 × IQR beyond the quartiles are outliers.

    IQR=47−36=11,[19.5,  63.5]\text{IQR} = 47 - 36 = 11,\quad [19.5,\; 63.5]
Formulas used
IQR=Q3−Q1\text{IQR} = Q_3 - Q_1
Outlier if x<Q1−1.5 IQR or x>Q3+1.5 IQR\text{Outlier if } x < Q_1 - 1.5\,\text{IQR} \text{ or } x > Q_3 + 1.5\,\text{IQR}
How this was checked
  • ✓ In order: min ≤ Q1 ≤ median ≤ Q3 ≤ max, with 27.3% of values at or below Q1 and 27.3% at or above Q3.

Quartiles use the median-of-halves method; some calculators interpolate and give slightly different values.

Frequently asked questions

What is the interquartile range?

Q3 − Q1, the spread of the middle half of the data. Unlike the range, outliers do not affect it.

How are outliers identified?

Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are outliers and are drawn as separate dots.

Why do different calculators give different quartiles?

There are several conventions. This one uses the median of each half, leaving out the overall median when there is an odd number of values.

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