Inclusive vs. Exclusive Interquartile Range

In this video I explain the difference between calculating an exclusive interquartile range and an inclusive interquartile range. While we generally use an exclusive interquartile range with an even set of scores, when we have an odd-numbered set of scores we can choose which method we'd like to use. The inclusive method will tend to give us a slightly smaller interquartile range by increasing the 25th percentile and decreasing the 75th percentile.

[@junede1005]

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[@bonanzawisdom0305]

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[@user-fd8hy4id3e]

Quality explanation, thank you!

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[@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!