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Concept
Seven-number summary
Summary
In descriptive statistics, the seven-number summary is a collection of seven summary statistics, and is an extension of the five-number summary. There are three similar, common forms.
As with the five-number summary, it can be represented by a modified box plot, adding hatch-marks on the "whiskers" for two of the additional numbers.
The following percentiles are (approximately) evenly spaced under a normally distributed variable:
the 2nd percentile (better: 2.15%)
the 9th percentile (better: 8.87%)
the 25th percentile or lower quartile or first quartile
the 50th percentile or median (middle value, or second quartile)
the 75th percentile or upper quartile or third quartile
the 91st percentile (better: 91.13%)
the 98th percentile (better: 97.85%)
The middle three values – the lower quartile, median, and upper quartile – are the usual statistics from the five-number summary and are the standard values for the box in a box plot.
The two unusual percentiles at either end are used because the locations of all seven values will be approximately equally spaced if the data is normally distributed Some statistical tests require normally distributed data, so the plotted values provide a convenient visual check for validity of later tests, simply by scanning to see if the marks for those seven percentiles appear to be equal distances apart on the graph.
Notice that whereas the extreme values of the five-number summary depend on the number of samples, this seven-number summary does not, and is somewhat more stable, since its whisker-ends are protected from the usual wild swings in the extreme values of the sample by replacing them with the more steady 2nd and 98th percentiles.
The values can be represented using a modified box plot. The 2nd and 98th percentiles are represented by the ends of the whiskers, and hatch-marks across the whiskers mark the 9th and 91st percentiles.
Arthur Bowley used a set of non-parametric statistics, called a "seven-figure summary", including the extremes, deciles, and quartiles, along with the median.
Official source
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