The EXAMINE command with the /PERCENTILES HAVERAGE option reports the 25th and 75th percentiles as 24.75 and 49.Īs an aside, Tukey appears to have invented the stem-and-leaf plot as a simple method of enumerating in a sorted fashion a batch of numbers in order to facilitate finding which data value is at a given _objects.Box ¶ class aph_objects. The boxplot as a result identifies the value 83 as an outlier and draws the upper whisker to the next highest value, 67. Notice the use of the truncate function to avoid having to deal with fractions other than. He defines the hinges as those values that lie at a depth midway between the median and the two extremes, or at depth (TRUNC(13.5) + 1)/2 = 7 counting in from each extreme, that is, at depths 7 and 20. Tukey would say that the median is at depth 13.5. The median is the average of the 13th and 14th cases, or 31. A simple example shows how the hinges are calculated. ![]() Tukey's book emphasized techniques that can be done by hand with a minimum of calculation. The two fences provide upper limits for the whisker length each whisker is drawn to that data value which is furthest from the median but still within the corresponding fence's distance from it. These values approximate, but in general do not match, the 25th and 75th percentiles reported by SPSS. SPSS follows his definition of the plot, where the upper and lower limits of the box are the Tukey hinges H1 and H2. The boxplot was developed by John Tukey and presented in his book Exploratory Data Analysis.
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