Hinges
The lower hinge is the median of the lower half of the data up to and including the median. The upper hinge is the median of the upper half of the data up to and including the median.
The hinges are the same as the quartiles unless the remainder when dividing the sample size by four is three (like 39 / 4 = 9 R 3).
The statement about the lower half or upper half including the median tends to be confusing to some students. If the median is split between two values (which happens whenever the sample size is even), the median isn't included in either since the median isn't actually part of the data.
Example 1: sample size of 20
The median will be in position 10.5. The lower half is positions 1 - 10 and the upper half is positions 11 - 20. The lower hinge is the median of the lower half and would be in position 5.5. The upper hinge is the median of the upper half and would be in position 5.5 starting with original position 11 as position 1 -- this is the original position 15.5.
Example 2: sample size of 21
The median is in position 11. The lower half is positions 1 - 11 and the upper half is positions 11 - 21. The lower hinge is the median of the lower half and would be in position 6. The upper hinge is the median of the upper half and would be in position 6 when starting at position 11 -- this is original position 16.
