Quartile

Quartiles split a sorted dataset into four equal-size parts:

• Q1 (25th percentile): one quarter below.
• Q2 (median, 50th): half below.
• Q3 (75th percentile): three quarters below.

Interquartile range (IQR) = $Q3 - Q1$, a robust measure of spread:

• Insensitive to outliers (unlike $\sigma$).
• Spans the "middle 50%" of the data.

The 5-number summary ($\min, Q1, Q2, Q3, \max$) is the basis of the box plot: box from Q1 to Q3 with median line, whiskers extending to the most extreme values within $1.5 \cdot IQR$, points beyond flagged as outliers.

Quartiles, like all percentiles, are non-parametric — no assumption about distribution shape, making them safer than mean/std for skewed or unknown distributions.