Inclusive vs. Exclusive Interquartile Range

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[@bonanzawisdom0305]

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[@DanGibson-i4u]

Quality explanation, thank you!

[@cuckoo_is_singing]

thank you for your good explanation: what is the Q1 of this data (n=12): 4 6 7 8.5 9 17 23 23 45 45 65 98 the median is 20, BUT for inclusive quartile I got Q1=8.125 and for exclusive 7.375 (for this one (I mean exclusive) excel used a linear interpolation. 13/4=3.25 --> 7+.25*(8.5-7), but for inclusive I can't find out how we can get to 8.125)

[@PsychExamReview]

For exclusive quartiles Excel uses n+1 when defining the quartile locations, as you've done, to get Q1 as 7.375 (the 3.25th location, between 7 and 8.5). But in the inclusive calculation, it's treating the starting point of your data as 4 and using n-1 to define the quartile locations. If we put these points on a line that starts at 4, we have 11 distances between 4 and 98. Q2 (the median) would be at (n-1)/2 or the 5.5th position starting from 4; exactly between 17 and 23, which is 20. Q1 would be at (n-1)/4 or 11/4, giving us the 2.75th position from 4. The 2.75th position from the starting point of 4 is between the values of 7 and 8.5, so it interpolates this value. There is a distance of 1.5 from 7 to 8.5, so it takes .75 times this distance (1.5), which is 1.125, and adds it to the 2nd position starting from 4, which is 7, giving us a 2.75th location of 8.125. Q3 would be at the 8.25th position, between the 8th and 9th positions, which are both 45, so no interpolation is needed and Q3 would be 45, the same value it would be with an exclusive calculation. Hope this makes sense!

[@niyiadewumi]

Very helpful.. thank you

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