MasterTool

Quartile Calculator

Calculate quartile using your data.

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What this tool does

Calculate quartile using your data. Linear-interpolation (type-7) quartiles, matching Excel QUARTILE.INC and NumPy defaults. Other textbooks use exclusive/Tukey hinges, which can differ slightly on small data sets — the method is stated so results can be checked.

How to use the Quartile Calculator

  1. Enter or select numbers (comma or whitespace separated).
  2. Read the calculated result; change any measurement to compare alternatives.

Formula

Q1, median (Q2) and Q3 by linear interpolation on the sorted data; IQR = Q3 − Q1
data
Numbers (comma or whitespace separated)

Linear-interpolation (type-7) quartiles, matching Excel QUARTILE.INC and NumPy defaults. Other textbooks use exclusive/Tukey hinges, which can differ slightly on small data sets — the method is stated so results can be checked.

Worked example

For quartile calculator, the following measurements illustrate the exact method: Numbers (comma or whitespace separated): 2,4,4,4,5,5,7,9.

Inputs

  • Numbers (comma or whitespace separated)2,4,4,4,5,5,7,9

Result

  • First quartile (Q1)4
  • Median (Q2)4.5
  • Third quartile (Q3)5.5
  • Interquartile range (IQR)1.5
  • Minimum2
  • Maximum9

Results explained

First quartile (Q1)
First quartile (Q1) from the formula above. Linear-interpolation (type-7) quartiles, matching Excel QUARTILE.INC and NumPy defaults. Other textbooks use exclusive/Tukey hinges, which can differ slightly on small data sets — the method is stated so results can be checked.
Median (Q2)
Median (Q2) from the formula above. Linear-interpolation (type-7) quartiles, matching Excel QUARTILE.INC and NumPy defaults. Other textbooks use exclusive/Tukey hinges, which can differ slightly on small data sets — the method is stated so results can be checked.
Third quartile (Q3)
Third quartile (Q3) from the formula above. Linear-interpolation (type-7) quartiles, matching Excel QUARTILE.INC and NumPy defaults. Other textbooks use exclusive/Tukey hinges, which can differ slightly on small data sets — the method is stated so results can be checked.
Interquartile range (IQR)
Interquartile range (IQR) from the formula above. Linear-interpolation (type-7) quartiles, matching Excel QUARTILE.INC and NumPy defaults. Other textbooks use exclusive/Tukey hinges, which can differ slightly on small data sets — the method is stated so results can be checked.
Minimum
Minimum from the formula above. Linear-interpolation (type-7) quartiles, matching Excel QUARTILE.INC and NumPy defaults. Other textbooks use exclusive/Tukey hinges, which can differ slightly on small data sets — the method is stated so results can be checked.
Maximum
Maximum from the formula above. Linear-interpolation (type-7) quartiles, matching Excel QUARTILE.INC and NumPy defaults. Other textbooks use exclusive/Tukey hinges, which can differ slightly on small data sets — the method is stated so results can be checked.

Frequently asked questions

Q1, median (Q2) and Q3 by linear interpolation on the sorted data; IQR = Q3 − Q1

Linear-interpolation (type-7) quartiles, matching Excel QUARTILE.INC and NumPy defaults. Other textbooks use exclusive/Tukey hinges, which can differ slightly on small data sets — the method is stated so results can be checked.

Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.

No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.

No. Every calculation, including the distribution algorithms, runs entirely in your browser.