Hi Jamie,

Quartiles can be confusing, especially since different authors and different textbooks have different definitions. I am going to explain using a process for finding the quartiles rather than using a definition in terms of percentages.

The second quartile Q₂ (sometimes called the median) is easy to find if the data is in sorted order. If the number of observations is odd, as in your case, you take the middle observation, in your case 65. If the number of observations is even then Q₂ is taken as half way between the middle two observations. So for example if your data set didn't include 99 and hence there were 18 observations then Q₂ would be (62 + 65)/2 = 63.5.

To find Q₃ you find the median of the upper half. Staying with the 18 observation data set above the upper half is 65,67,70,75,81,82,86,89,94 and the median of this data set is 81 so if the data set were 36,45,49,53,55,56,59,61,62,65,67,70,75,81,82,86,89,94 then Q₃ = 81. With your 19 observation data set divided into two equal parts by the median

36,45,49,53,55,56,59,61,62,65,67,70,75,81,82,86,89,94,99

what is the upper half? Is it 67,70,75,81,82,86,89,94,99 or 65,67,70,75,81,82,86,89,94,99?
If it is the former then Q₃, being the median of 67,70,75,81,82,86,89,94,99 is 82.
If the upper half is 65,67,70,75,81,82,86,89,94,99 then the median is (81 + 82)/2 = 81.5.

It seems that your textbook author and your teacher use the second process and get Q₃ = 81.5

I hope this helps,
Penny