Solution 12185: Algorithm Used by TI Graphing Calculators for Computing Quartiles.
What method do TI graphing calculators use for computing quartiles?
TI graphing calculators compute quartiles by simply averaging the values of adjacent ordered measurements.
Consider this example using the data {14, 29, 32, 38, 41, 45, 68, 71, 74, 83, 86, 87}. TI calculators use the formula .25(n+1) to calculate the position of the lower quartile. In this case, it is at the position 3.25. Instead of returning an "exact" position, ((38-32)*.25) + 32 = 33.5, TI calculators return the "average" position between the 3rd and 4th ordered measurements. Here, the TI calculators calculate the 1st Quartile as (32+38)/2 = 35, instead of the "exact" position (33.5) used in some statistical software packages.
Various methods can be used to compute quartiles. TI calculators use a method taught most often at the high school level.
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