Percentile Calculator
Calculate percentile rank, percentile value, and quartiles from data. Find what percentage of values fall below a given data point, or find the value at any percentile (Q1, Q2, Q3).
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Percentile Calculator | — | Percentile rank = (B/n) × 100 | percentile (0-100) |
Step-by-Step Examples
Dataset: 55,65,70,75,80,85,90,95. Where does score 75 rank?
- Values below 75: 55,65,70 → 3 values
- Percentile = 3/8 × 100 = 37.5th percentile
- Score of 75 is at the 37.5th percentile
- Above 37.5% of the class
Same dataset (n=8). What score is at the 90th percentile?
- Index = 0.90 × (8-1) = 6.3
- Value = data[6] + 0.3×(data[7]-data[6])
- = 90 + 0.3×(95-90) = 90 + 1.5 = 91.5
- 90th percentile = 91.5
Quartiles from dataset: Q1=65, Q2=77.5, Q3=87.5.
- IQR = 87.5 - 65 = 22.5
- Lower fence = 65 - 1.5×22.5 = 31.25
- Upper fence = 87.5 + 1.5×22.5 = 121.25
- Any values outside 31.25-121.25 are outliers
Real-World Applications
Common Mistakes to Avoid
75th percentile means you scored higher than 75% of others. It is not your score as a percentage. A 75th percentile score could be 60% or 95% correct depending on the test.
Excel, Python, R, and textbooks use slightly different interpolation methods for percentiles. For small datasets, the method can give noticeably different answers.
Values beyond Q1-1.5×IQR or Q3+1.5×IQR are potential outliers. Always investigate WHY before removing them — they may be real and important data points.
Frequently Asked Questions
Related Math Calculators
Formula Explorer connections
Interpretation: This formula summarizes data, models uncertainty or supports inference about a population or random process. Assumption: The sampling design and distribution assumptions must match the data. Independence, sample size, outliers and measurement quality can materially affect interpretation.