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seven number summary wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 seven number summary 2 bowley s seven figure summary 3 tukey s seven number summary 4 see also 5 footnotes 6 references toggle the table of contents seven number summary 2 languages فارسی français edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia 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 common forms all based on percentiles evaluated at different percentage values 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 seven number summary edit the following percentiles are approximately evenly spaced under a normally distributed variable normal distribution seven summary numbers nr approximate percentile more precise percentile position alternate name s 7 98th 97 85 upper whisker top end 6 91st 91 13 upper whisker crosshatch 5 75th 75 00 box upper edge upper quartile or third quartile 4 50th 50 00 box bisector mid line median middle value or second quartile 3 25th 25 00 box lower edge lower quartile or first quartile 2 9th 8 87 lower whisker crosshatch 1 2nd 2 15 lower whisker bottom end 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 a 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 plot 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 bowley s seven figure summary edit arthur bowley used a set of non parametric statistics called a seven figure summary including the extremes deciles and quartiles along with the median 1 thus the numbers are bowley s seven summary figures 1 nr percentile alternate name s 1 0 sample minimum nominal highest zero th percentile 2 10 first decile 3 25 lower quartile or first quartile 4 50 median middle value or second quartile 5 75 upper quartile or third quartile 6 90 last decile 7 100 sample maximum nominal lowest hundredth percentile note that the middle five of the seven numbers are very nearly the same as for the seven number summary above the addition of the deciles allow one to compute the interdecile range which for a normal distribution can be scaled to give a reasonably efficient estimate of standard deviation and the 10 midsummary which when compared to the median gives an idea of the skewness in the tails tukey s seven number summary edit john tukey used a seven number summary consisting of the extremes octiles quartiles and the median 2 the seven numbers are tukey s seven summary figures 2 nr percentile alternate name s 1 0 sample minimum nominal highest zero th percentile 2 12 5 first octile 3 25 0 lower quartile or first quartile 4 50 0 median middle value or second quartile 5 75 0 upper quartile or third quartile 6 87 5 last octile 7 100 sample maximum nominal lowest hundredth percentile note that the middle five of the seven numbers can all be obtained by successive partitioning of the ordered data into subsets of equal size extending the seven number summary by continued partitioning produces the nine number summary the eleven number summary and so on see also edit three point estimation stanine footnotes edit the seven equally spaced percentiles with three digits of precision are 2 15 8 87 25 0 50 0 75 0 91 13 and 97 85 if one desires to identify a symmetric distribution different from the normal or gaussian distribution the listed outer pairs of quantiles 2 15 and 8 87 on the lower whisker and on the upper whisker 91 13 and 97 85 may be replaced by quantiles from the other desired distribution whose argument spacing has been calculated to match the spacing between the median and the quartiles references edit 1 2 bowley a 1920 elementary manual of statistics 3rd ed p 62 the seven positions are the maximum and minimum median quartiles and two deciles 1 2 tukey j 1977 exploratory data analysis addison wesley publishing company p 53 isbn 978 0 201 07616 5 retrieved from https en wikipedia org w index php title seven number_summary oldid 1339470562 category summary statistics this page was last edited on 20 february 2026 at 18 53 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and 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