Question 1

What is the difference between percentile and percentage?

Accepted Answer

A percentage is a proportion out of 100 — e.g., "you answered 80% of questions correctly." A percentile is a position in a ranked distribution — e.g., "you scored at the 80th percentile, meaning you scored higher than 80% of test-takers." A student who gets 80% correct on an easy test might only be at the 30th percentile if most others also scored high.

Question 2

What are quartiles and how do they relate to percentiles?

Accepted Answer

Quartiles divide a sorted dataset into four equal parts. Q1 (first quartile) is the 25th percentile — 25% of data falls below it. Q2 (second quartile) is the 50th percentile — the median. Q3 (third quartile) is the 75th percentile. The interquartile range (IQR = Q3 − Q1) contains the middle 50% of the data and is a robust measure of spread, unaffected by extreme outliers.

Question 3

Which percentile calculation method does this calculator use?

Accepted Answer

This calculator uses the linear interpolation method (also called the "inclusive" method), which is standard in most statistics software (Excel PERCENTILE.INC, R quantile type 7, Python numpy default). The position index is computed as p/100 × (n−1), and if it falls between two values, the result is interpolated. Alternative methods (exclusive, nearest rank) exist and can give slightly different results for small datasets.

Question 4

How do you interpret IQR for outlier detection?

Accepted Answer

The IQR is used in the Tukey fence method to identify outliers: any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is considered a mild outlier; beyond Q1 − 3×IQR or Q3 + 3×IQR is an extreme outlier. This is the method used by box plots. Because IQR is based only on the middle 50% of data, it is resistant to the outliers it is trying to detect.

Question 5

What does the 90th percentile mean in practice?

Accepted Answer

If your score is at the 90th percentile, you performed equal to or better than 90% of the reference group. In income terms, the 90th percentile household income in the US means that household earns more than 90% of all households. In child growth charts, a child at the 90th percentile for height is taller than 90% of children of the same age and sex.

Question 6

How are percentiles used in standardised tests like SAT or GRE?

Accepted Answer

Standardised test scores are always reported with a percentile rank alongside the raw score. A GRE Verbal score of 163 corresponds to approximately the 91st percentile — you scored higher than 91% of test takers in the reference group (typically the last 3 years of test takers). This contextualises the raw score: a 163 out of 170 sounds high, but the percentile tells you exactly where you stand relative to your peer group.

Percentile	Also Known As	Meaning
0th	Minimum	0% of values fall below — the smallest value
25th	Q1, First Quartile	25% of data is below this value
50th	Q2, Median	Middle of the distribution — half above, half below
75th	Q3, Third Quartile	75% of data is below this value
90th	D9 (9th Decile)	Common benchmark in income, test scores
95th	—	Used in clinical ranges, speed benchmarks
99th	—	Top 1% — elite performance benchmark
100th	Maximum	100% of values fall at or below — the largest value

Goal	Percentile	Z-Score	IQR
Compare an individual to a reference group	✓	✓	—
Data is normally distributed	—	✓ Preferred	—
Data is skewed or non-normal	✓	Misleading	✓
Identify outliers	✓ Tukey fences	\|z\|>3 rule	✓
Standardise across different scales	—	✓	—
Describe middle 50% spread	✓ P75−P25	—	✓ Same

Percentile Calculator

Formula

Key Percentile Landmarks

Percentile vs Z-Score vs IQR — Which to Use?

Common Mistakes with Percentiles

Case Study: Raw Score Cutoffs vs Percentile Rank in a School District

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