Percentiles and Quartiles

What are percentiles?

The $k$th percentile is the value below which $k\%$ of the data falls.

• 25th percentile = Q1 (first quartile)
• 50th percentile = Q2 (median)
• 75th percentile = Q3 (third quartile)

Step-by-step: Finding percentiles

Step 1 — Sort the data from smallest to largest.

Step 2 — Compute the position: $L = \frac{k}{100} \times n$, where $k$ is the percentile and $n$ is the number of data points.

Step 3 — If $L$ is not a whole number, round up to get the position. If it is a whole number, average the values at positions $L$ and $L+1$.

Example with 20 scores

For Q1 (25th percentile): $L = 0.25 \times 20 = 5$. Average values at positions 5 and 6.

For Q2 (50th percentile): $L = 0.50 \times 20 = 10$. Average values at positions 10 and 11.

For Q3 (75th percentile): $L = 0.75 \times 20 = 15$. Average values at positions 15 and 16.

Interpretation

If your score is at the 90th percentile, you scored higher than 90% of test-takers.

Try it in the visualization

The sorted data is displayed. Q1, Q2, Q3 are marked with vertical lines. Each quartile contains exactly 25% of the data.