- Seven-number summary
In

descriptive statistics , the**seven-number summary**is a collection of sevensummary statistics , and is a modification or extension of thefive-number summary . There are two common forms.**(Parametric) Seven-number summary**The following numbers are

parametric statistics for a normally distributed model:

# the 2^{nd}percentile

# the 9^{th}percentile

# the 25^{th}percentile or lower quartile or "first quartile"

# the 50^{th}percentile ormedian (middle value, or "second quartile")

# the 75^{th}percentile or upper quartile or "third quartile"

# the 91^{st}percentile

# the 98^{th}percentile The unusual percentiles are used because the locations of all seven values will be 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 locations of those seven percentiles appear to be equally spaced.

Notice that whereas the

five-number summary makes no assumptions about the distribution of the data, theseven-number summary is based on thenormal distribution , and is not especially appropriate when normal data is not expected.The values can be represented using a modified

box plot . The 2^{nd}and 98^{th}percentiles are represented by the ends of the whiskers, and hatch-marks across the whiskers mark the 9^{th}and 91^{st}percentiles.**Bowley’s seven-figure summary**Arthur Bowley used a set ofnon-parametric statistics , called a "seven-figure summary", including the extremes,decile s andquartile s, along with the median - see his "Elementary Manual of Statistics" (3rd edn., 1920), p.62 - he defines "the maximum and minimum, median, quartiles and two deciles" as the "seven positions").Thus the numbers are:

# the minimum

# the 10^{th}percentile (firstdecile )

# the 25^{th}percentile or lower quartile or "first quartile"

# the 50^{th}percentile ormedian (middle value, or "second quartile")

# the 75^{th}percentile or upper quartile or "third quartile"

# the 90^{th}percentile (lastdecile )

# the maximum**ee also***

Stanine

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