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Percentile
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==The normal distribution and percentiles== [[File:Standard deviation diagram.svg|325px|thumb|Representation of the [[68β95β99.7 rule|three-sigma rule]]. The dark blue zone represents observations within one [[standard deviation]] (Ο) to either side of the [[mean]] (ΞΌ), which accounts for about 68.3% of the population. Two standard deviations from the mean (dark and medium blue) account for about 95.4%, and three standard deviations (dark, medium, and light blue) for about 99.7%.]] The methods given in the ''calculation methods'' section (below) are approximations for use in small-sample statistics. In general terms, for very large populations following a [[normal distribution]], percentiles may often be represented by reference to a normal curve plot. The normal distribution is plotted along an axis scaled to [[standard deviation]]s, or sigma (<math>\sigma</math>) units. Mathematically, the normal distribution extends to negative [[infinity]] on the left and positive infinity on the right. Note, however, that only a very small proportion of individuals in a population will fall outside the β3''Ο'' to +3''Ο'' range. For example, with human heights very few people are above the +3''Ο'' 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, β3''Ο'' is the 0.13th percentile, β2''Ο'' the 2.28th percentile, β1''Ο'' the 15.87th percentile, 0''Ο'' the 50th percentile (both the mean and median of the distribution), +1''Ο'' the 84.13th percentile, +2''Ο'' the 97.72nd percentile, and +3''Ο'' the 99.87th percentile. This is related to the [[68β95β99.7 rule]] or the three-sigma rule. Note that in theory the 0th percentile falls at negative infinity and the 100th percentile at positive infinity, although in many practical applications, such as test results, natural lower and/or upper limits are enforced.
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