Quartiles and Percentiles: Reading Data by Rank Position

Quartiles and percentiles show which values fall below a given percentage of your sorted data, and they form the basis of the box plot.

What is a percentile?

When you sort your data from smallest to largest, the kth percentile is the value below which k% of the observations fall. For example, the 90th percentile is the point below which 90% of the data lies.

Quartiles

Quartiles are the three points that split the data into four equal parts: Q1 (25th percentile), Q2 (the median, 50th percentile), and Q3 (75th percentile). The difference between Q3 and Q1 is the interquartile range (IQR) — a spread measure that’s more resistant to outliers than the standard deviation.

Example: If a store’s daily sales data has Q1 = $120 and Q3 = $210, the IQR is $90 — the width of the middle 50% of sales.

How it relates to the box plot

• The box’s bottom and top edges mark Q1 and Q3.
• The line inside the box marks the median (Q2).
• Whiskers typically extend to 1.5×IQR; points beyond that are flagged as outliers.

Quartiles offer a more reliable way to summarize skewed distributions, where the mean and standard deviation are pulled around by outliers — which is why they’re a common choice for right-skewed variables like income, price, or duration.