# Percentile

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The xth percentile is the value that x% of a observed values of a variable are less than or equal to. For example, if 90% of people have an income of less than or equal to \$100,000 per year then 90th percentile is \$100,000.

## Technical details

• The 50th percentile is known as the Median.
• Where there the data is discrete or sample sizes are small, there is no unambiguous method of computing a percentile. For example, there is no unambiguous way of computing the 90th percentile of three numbers. Numerous different methods have been developed for this problem, such as interpolating and fitting values by assuming a distribution.
• When the data is weighted methods based on either interpolation or the fitting of values to a distribution need to be used.
• Where the percentiles are computed using either interpolation or the fitting of values to a distribution the only situations where it will make a substantive difference to interpretation are situations where the percentile is an inappropriate way of describing the data (and, it is typically obvious when this this is the case).