Britannica Sources used in this answer

How do percentiles show the spread of data values?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

statistics Figure 1: A bar graph showing the marital status of 100 individuals.

Percentiles describe the spread of data by indicating the relative position of a specific value within a dataset, showing what percentage of observations fall below that point. By dividing an ordered dataset into 100 equal parts, percentiles allow statisticians to map the distribution of values from the minimum to the maximum.12

To better visualize this spread, researchers often use a five-number summary, which utilizes specific percentiles to describe the distribution's variability:1

Minimum: The lowest observation.1
First Quartile ( $Q_{1}$ ): The 25th percentile.13
Median ( $Q_{2}$ ): The 50th percentile, representing the central value.13
Third Quartile ( $Q_{3}$ ): The 75th percentile.13
Maximum: The highest observation.1

These quartiles are frequently visualized using a box-and-whisker plot. This graph uses the quartiles to form a box, while lines (whiskers) extend to the minimum and maximum values. This technique effectively reveals the central tendency, the symmetry or skewness of the data, and the presence of any outliers.3