Why is the 75th percentile of 1-10 not exactly 7.5 or 8?

The calculator uses linear interpolation between the two closest ranked values rather than simply picking the nearest data point, which is why the 75th percentile of 1-10 comes out to 7.75 instead of a whole number.

How is the interquartile range (IQR) used?

IQR = Q3 − Q1, the range of the middle 50% of the data. It's commonly used to detect outliers (values more than 1.5×IQR below Q1 or above Q3) and is less sensitive to extreme values than the full range.

Percentile Calculator

Find any percentile, quartiles and the interquartile range (IQR) of a dataset.

How this is calculated

Linear-interpolation percentile: rank = (P ÷ 100) × (n − 1), interpolated between adjacent sorted values

Assumptions used in this calculation

Interpolation method: Percentiles use linear interpolation between adjacent sorted values (the same method as Excel's PERCENTILE.INC / NumPy's default "linear" method), rather than the "nearest rank" method some textbooks use.

About this calculator

The percentile calculator finds any percentile of a dataset using linear interpolation, along with Q1, median, Q3 and the interquartile range (IQR).

Worked example

1-10, 75th percentile

Result: 7.75

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Frequently asked questions

Why is the 75th percentile of 1-10 not exactly 7.5 or 8?

How is the interquartile range (IQR) used?

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