Percentile Calculator
Calculate any percentile (1st-99th) from your dataset with step-by-step solutions. Display single or multiple percentiles for comprehensive statistical analysis.
Percentile Calculator
Separate values with commas
Solution:
Enter a dataset and click Calculate to see percentile analysis
What is a Percentile?
A percentile is a statistical measure that indicates the value below which a given percentage of observations in a dataset fall. For example, the 75th percentile (P₇₅) is the value below which 75% of the data falls. Percentiles are widely used in statistics, standardized testing, growth charts, and data analysis to understand the relative standing of a value within a dataset.
Percentile Formula:
Position = (p / 100) × (n + 1)
Where p = desired percentile (1-99) and n = number of data points
If the position is not a whole number, interpolate between the two nearest values.
Common Percentiles and Their Meanings
| Percentile | Notation | Meaning | Also Known As |
|---|---|---|---|
| 25th | P₂₅ | 25% of data below this value | First Quartile (Q₁) |
| 50th | P₅₀ | 50% of data below this value | Median (Q₂) |
| 75th | P₇₅ | 75% of data below this value | Third Quartile (Q₃) |
| 90th | P₉₀ | 90% of data below this value | Top 10% |
| 95th | P₉₅ | 95% of data below this value | Top 5% |
| 99th | P₉₉ | 99% of data below this value | Top 1% |
How to Calculate Percentiles
Step-by-Step Method
- Sort the Data: Arrange all values in ascending order from smallest to largest
- Calculate Position: Use the formula: Position = (p / 100) × (n + 1)
- Find the Value:
- If position is a whole number, use the value at that position
- If position is fractional, interpolate between the two nearest values
- Interpret: The result tells you the value below which p% of the data falls
Example Calculation
Dataset: 15, 20, 35, 40, 50 (already sorted, n = 5)
Find P₅₀ (50th percentile):
Position = (50 / 100) × (5 + 1) = 0.5 × 6 = 3
The 3rd value in the sorted list is 35
P₅₀ = 35 (This is also the median)
Percentiles vs Quartiles vs Deciles
Percentiles
- • Divide data into 100 parts
- • P₁, P₂, ..., P₉₉
- • Most granular measure
- • Used in standardized tests
- • Best for large datasets
Quartiles
- • Divide data into 4 parts
- • Q₁ (25th), Q₂ (50th), Q₃ (75th)
- • Special case of percentiles
- • Used in box plots
- • IQR = Q₃ − Q₁
Deciles
- • Divide data into 10 parts
- • D₁, D₂, ..., D₉
- • D₁ = P₁₀, D₂ = P₂₀, etc.
- • Used in economics
- • Medium granularity
Applications of Percentiles
Percentiles are used extensively across many fields to understand data distribution and relative standing:
Education & Testing
- • SAT, GRE, GMAT score interpretation
- • Student performance ranking
- • Grade distribution analysis
- • Benchmark comparisons
Healthcare
- • Growth charts for children
- • Blood pressure ranges
- • BMI percentiles by age
- • Clinical test results
Business & Finance
- • Income distribution
- • Sales performance metrics
- • Risk assessment (VaR)
- • Market analysis
Data Science
- • Outlier detection
- • Data distribution analysis
- • Feature engineering
- • Model evaluation
Frequently Asked Questions
What is the difference between percentile and percentage?
A percentage represents a proportion out of 100, while a percentile indicates the position in a distribution. For example, scoring 80% on a test means you got 80 out of 100 points, but being in the 80th percentile means you scored better than 80% of test-takers.
Is the 50th percentile the same as the median?
Yes, the 50th percentile (P₅₀) is exactly the same as the median. It represents the middle value of a dataset where 50% of values fall below and 50% fall above. The median is also known as the second quartile (Q₂).
Why can't we calculate the 0th or 100th percentile?
The 0th percentile would mean that 0% of data falls below that value (which would be less than the minimum), and the 100th percentile would mean 100% of data falls below it (which would be greater than the maximum). These aren't meaningful measures. Instead, we use the actual minimum and maximum values of the dataset.
What does it mean to be in the 95th percentile?
Being in the 95th percentile means you scored better than 95% of the population. Only 5% scored higher than you. This is considered a very high ranking and is often used to identify exceptional performance or outliers in positive contexts.
How do you interpolate when the position is not a whole number?
When the calculated position falls between two data points (e.g., position 3.5), we interpolate by taking a weighted average. For position 3.5, we'd use 50% of the 3rd value and 50% of the 4th value. The formula is: value = lower_value + (fraction × (upper_value − lower_value)).
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