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If you score in the 90th percentile on a standardized exam, that doesn't mean you got 90% of the questions correct. It means you scored higher than 90% of all students who took the test.
Measures of position tell us where a single score stands relative to an entire group, turning raw scores into meaningful comparisons.
How do we mathematically slice any sorted dataset into exact percentage benchmarks?

Percentiles and Location

A percentile PkP_k is the data value below which kk percent of the observations fall in an ordered dataset. In 1885, polymath Francis Galton introduced percentiles to describe human traits when data did not form a neat bell curve.
To find the value at percentile kk, we first calculate its index locator L=k100×nL = \frac{k}{100} \times n, where nn is the total number of ordered values. If LL is a whole number, we average the LL-th and (L+1)(L+1)-th values; if LL is a decimal, we round up to the next integer position.
What happens when we split an ordered dataset into four equal quarters instead of a hundred slices?

The Three Quartiles

Quartiles divide ordered data into four equal parts using three specific boundary cutoffs: Q1Q_1, Q2Q_2, and Q3Q_3.
The first quartile (Q1Q_1) is the 25th percentile, the second quartile (Q2Q_2) is the 50th percentile or median, and the third quartile (Q3Q_3) is the 75th percentile.
Why do standard measures of spread like the total range fail when extreme values or outliers enter the picture?