Percentile - The Normal Curve and Percentiles

The Normal Curve and Percentiles

The methods given above are approximations for use in small-sample statistics. In general terms, for very large populations percentiles may often be represented by reference to a normal curve plot. The normal curve is plotted along an axis scaled to standard deviation, or sigma, units. Mathematically, the normal curve extends to negative infinity on the left and positive infinity on the right. Note, however, that a very small portion of individuals in a population will fall outside the −3 to +3 range.

In humans, for example, a small portion of all people can be expected to fall above the +3 sigma height level.

Percentiles represent the area under the normal curve, increasing from left to right. Each standard deviation represents a fixed percentile. Thus, rounding to two decimal places, −3 is the 0.13th percentile, −2 the 2.28th percentile, −1 the 15.87th percentile, 0 the 50th percentile (both the mean and median of the distribution), +1 the 84.13th percentile, +2 the 97.72nd percentile, and +3 the 99.87th percentile. Note that the 0th percentile falls at negative infinity and the 100th percentile at positive infinity.