Quartile

One of the three cut points that split sorted data into four equal-sized groups.

Visual intuition

sort first

middle seat

100

Median = the value in the middle position

Quartiles are cut points in the sorted line: a quarter, half, and three-quarters of the way along — the middle one is the median.

Example

For the nine sorted values 2, 3, 5, 6, 8, 10, 12, 15, 20, the quartiles are Q1 = 4, = 8, and Q3 = 13.5, so the middle half spans 4 to 13.5.

How It Works

Sort the data and cut it into quarters: the first quartile (Q1) has 25% of values below it, the second is the , and the third (Q3) has 75% below. The middle half of the data lives between Q1 and Q3 — a span called the interquartile range — which makes quartiles a compact, -resistant way to describe both center and spread. Box plots are drawn from exactly these numbers.

Concepts

Summary Statistics

Summary statistics compress a dataset into numbers such as the mean, variance, correlation, or regression line. They are useful, but they can hide shape, outliers, clusters, and curved relationships that a graph would reveal immediately.

Lessons

Four small scatterplots with similar summary lines but different shapes.

Summaries Need Pictures

Means, variances, correlations, and regression lines can match while the underlying data tell completely different stories.

Related Facts

Data Tricks

5 min · easy

Bars rising from short to tall, a pointer on the middle bar and a dashed line sitting high above most of them.

Mean vs median: which average should you use?

The mean shares the total equally. The median finds the middle case. In skewed data, those can tell very different stories.