Statistics Calculator: Quartiles

Use this calculator to compute the quartiles from a set of numerical values.

Quartiles Calculator

Instructions

This calculator computes the first, second and third quartiles from a data set:

To calculate the quartiles from a set of values, enter the observed values in the box above. Values must be numeric and may be separated by commas, spaces or new-line. Data copied from from another document may also be pasted in the text box. You may ignore the Population/Sample selector because it is only relevant when calculating the variance or the standard deviation. Press the "Submit Data" button to perform the computation. To clear the calculator and enter a new data set, press "Reset".

What are the quartiles

The first quartile, or 25th percentile x_L (also written as Q₁), is the number for which 25% of values in the data set are smaller than x_L.

The second quartile or 50th percentile, x_m (also written as Q₂) is also known as the median. It represents the value for which 50% of observations are lower and 50% are higher.

The third quartile or 75th percentile, x_H (Q₃) is the value such that 75% of the observations are less than x_H

How are quartiles calculated

This calculator uses the following system to find the quartiles:

n is the number of observations. x₁, x₂ ... x_n are the values sorted from the lowest to the highest.

By 'integer' we mean the integer portion and by decimal, the decimal portion (the part of the number following the decimal point) of a number.

First quartile formulas

If $\frac{1}{4}(n+1)$ is integer, the first quartile is $x_{\frac{1}{4}(n+1)}$

If $\frac{1}{4}(n+1)$ is not integer, the first quartile is interpolated using this formula:
$x_{integer(\frac{1}{4}(n+1))}+(x_{integer(\frac{1}{4}(n+1))+1}) (decimal(\frac{1}{4}(n+1)))$

Third quartile formulas

If $\frac{3}{4}(n+1)$ is integer, the third quartile is $x_{\frac{3}{4}(n+1)}$

If $\frac{3}{4}(n+1)$ is not integer, the third quartile is interpolated using this formula:
$x_{integer(\frac{3}{4}(n+1))}+(x_{integer(\frac{3}{4}(n+1))+1}) (decimal(\frac{3}{4}(n+1)))$