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Quartile of Numbers

Tool to calculate the quartile value from a list of values. The quartile of a list of numbers is a statistical value that partially illustrates the distribution of numbers in the list.

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Quartile of Numbers -

Tag(s) : Statistics, Data Processing

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# Quartile of Numbers

## Quartiles Calculator

### What is a quartile?

Quartiles (or the four quarters) are three values that separate a list of sorted numbers composed of $n$ values $X = \{ x_1, x_2, \dots, x_n \}$ into $4$ (four) equal parts: the first quartile (25%, the lower quartile), the second quartile (50%) also called the median, and the third quartile (75%, the higher quartile).

### How to compute a quartile? (Definition)

Automatic method: on dCode, enter (or copy-paste) the list of numbers and click on Calculate.

Manual method: From a list of $N$ elements sorted by ascending order, calculate $q_1 = N / 4$, $q_2 = N / 2$ and $q_3 = 3 N / 4$. Locate the elements of the list in position $q_i$, the value of the element is the $i$-th quartile.

NB: if $q_i$ is not an integer, take the average between the element just before and the element just after. It is also possible to take the closest value in the list (less rigorous method).

Example: The list of 8 elements: 11,3,5,7,19,13,17,2 is sorted by ascending order 2,3,5,7,11,13,17,19. Its quartiles are 4, 9 and 15, this means that there are 25% of the values lower than 4 and 75% higher than 4, and that there are 25% of the values greater than 15 and 75% lower.

### When to use the quartiles?

Quartiles are used to describe the dispersion of a series. If the gap between 2 quartiles is small, then many values are in this zone.

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