How to Compute Percentile Value from Sorted List in Python

Compute any percentile value from a sorted list using linear interpolation between ranks.

Easy Python 3.9+ Aug 9, 2026 Lists & loops 16 views 0 copies

percentile statistics interpolation sorted-list lists

Python code

25 lines

Python 3.9+

def percentile(sorted_data, percentile_value):
    """Return the value below which `percentile_value`% of data falls."""
    if not sorted_data:
        raise ValueError("Cannot compute percentile of empty list")
    if not 0 <= percentile_value <= 100:
        raise ValueError("Percentile must be between 0 and 100")

    k = (len(sorted_data) - 1) * (percentile_value / 100.0)
    lower = int(k)
    upper = lower + 1

    if upper >= len(sorted_data):
        return sorted_data[lower]
    if lower == upper:
        return sorted_data[lower]

    weight = k - lower
    return sorted_data[lower] * (1 - weight) + sorted_data[upper] * weight


if __name__ == "__main__":
    data = [12, 15, 18, 21, 24, 29, 33, 40]
    for p in [0, 25, 50, 75, 100]:
        result = percentile(data, p)
        print(f"{p}th percentile: {result}")

Output

stdout

0th percentile: 12
25th percentile: 15.0
50th percentile: 22.5
75th percentile: 26.25
100th percentile: 40

How it works

This function implements the linear interpolation method (also called the NIST or Excel PERCENTILE.INC method). The formula k = (n-1) * (p/100) finds a fractional rank position in the sorted list. When k is a whole number, it returns that exact value; otherwise, it interpolates between the lower and upper neighbors at that fractional position. The guard clauses handle edge cases like empty lists and out-of-range percentiles, making the function safe for production use. The main block demonstrates output for common percentiles, showing both exact and interpolated results.

Common mistakes

Forgetting to validate that the input list is sorted before calling the function
Using integer division (//) instead of float division (/) when computing `k`, which truncates interpolation
Failing to handle the edge case where `upper` index goes beyond the list length for 100th percentile

Variations

Use NumPy: `numpy.percentile(data, p)` when already using scientific libraries
Implement nearest-rank method by rounding `k` up instead of interpolating

Real-world use cases

Calculating latency SLOs (e.g., p95, p99) from sorted API response time logs in observability dashboards. (193 chars)
Analyzing test scores or salary bands where business rules require thresholds like the 75th percentile cutoff. (146 chars)
Determining performance benchmarks and capacity planning by finding percentiles of resource usage metrics. (163 chars)

How to Compute Percentile Value from Sorted List in Python

Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

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Common mistakes

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Real-world use cases

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