Calculate Percentiles with Multiple Methods and Step-by-Step Derivation
Enter data values (comma separated)
Percentile to calculate (0-100)
Results
Linear Interpolation
Nearest Rank
Q1 (25th)
Q2 (50th, Median)
Q3 (75th)
IQR
Sorted Data
Step-by-Step Derivation
Percentile Formulas
Linear Interpolation: i = (p/100)(n-1), P = xⱼ + (i-j)(xⱼ₊₁ - xⱼ)
Nearest Rank: i = ceil((p/100)n), P = xᵢ
Linear interpolation is the most common method and is used in Excel and many statistical software.
⚠Different percentile methods can give slightly different results. Linear interpolation is generally preferred.
What are Percentiles?
Percentiles are measures indicating the value below which a given percentage of observations in a group of observations fall. They are used to understand the distribution and relative standing of data.
Relative Standing
Shows how a value compares to others
Quartiles
Divide data into 4 equal parts
Robust Measure
Less affected by outliers than mean
IQR
Interquartile range = Q3 - Q1
💡 Example: For data [1,2,3,4,5,6,7,8,9,10], the 75th percentile using linear interpolation is 7.75.
Applications
StatisticsEducationHealthcareFinanceAdmissions
Frequently Asked Questions
What is a percentile?▼
A percentile is a measure indicating the value below which a given percentage of observations fall. P50 is the median.
How to calculate percentiles?▼
Common methods: linear interpolation, nearest rank, exclusive method. Each gives slightly different results for small datasets.
What are quartiles?▼
Quartiles divide data into 4 parts: Q1 (25th), Q2 (50th, median), Q3 (75th). Interquartile range = Q3 - Q1.
Why use percentiles?▼
Percentiles show relative standing, identify outliers, normalize comparisons across different distributions, and are robust to outliers.
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