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In statistics, a k-th percentile, also known as percentile score or centile, is a score below which a given percentage k of scores in its frequency distribution falls ("exclusive" definition) or a score at or below which a given percentage falls ("inclusive" definition); i.e. a score in the k-th percentile would be above approximately k% of all scores in its set.
The figure illustrates the percentile rank computation and shows how the 0.5 × F term in the formula ensures that the percentile rank reflects a percentage of scores less than the specified score. For example, for the 10 scores shown in the figure, 60% of them are below a score of 4 (five less than 4 and half of the two equal to 4) and 95% are ...
Third quartile (Q 3 or 75th percentile): also known as the upper quartile q n (0.75), it is the median of the upper half of the dataset. [ 7 ] In addition to the minimum and maximum values used to construct a box-plot, another important element that can also be employed to obtain a box-plot is the interquartile range (IQR), as denoted below:
The lower middle class consists of those in the 20th to 40th percentile of household income. ... this group down even further into those in the 80th to 90th and the 90th to 100th income ...
Moreover, some software programs (including Microsoft Excel) regard the minimum and maximum as the 0th and 100th percentile, respectively. However, this broader terminology is an extension beyond traditional statistics definitions.
The last of these, n / n, corresponds to the 100th percentile – the maximum value of the theoretical distribution, which is sometimes infinite. Other choices are the use of ( k − 0.5) / n , or instead to space the n points such that there is an equal distance between all of them and also between the two outermost points and the edges of the ...
For example, the Fed data shows that median retirement account balances of those earning in the lowest 20% totals $17,500, while the median value of retirement plans for those earning in the 90th ...
The definition given for the percentile is "the value below which a given percentage of observations in a group of observations fall", yet in all of the worked examples, the 100th percentile is assumed to be the largest element in the set. despite at least one of the observations not falling below that value.