Hello Mandi_MooQuartile -- from Wolfram MathWorld.
The method I've always thought the best is to add 1; then
- take a quarter of the result to get the position of the first quartile;
- take a half to get the position of the median;
- and take three-quarters to get the third quartile.
For example, if there are 11 items, .
Then, using the method I've just described, the median (which is sometimes called the second quartile) is in position. This makes sense as the middle item, because there are then 5 items on either side (5 + 1 + 5 = 11).
The first quartile (which I think of as the median of the lower 5 of these items) is in position. Within the lower 5 items, then, the third one has two either side - so it's their median.
And the third quartile (the median of the top 5 items) is in position.
This gives the following picture: where the circled dots represent the quartiles. You'll see these are evenly spaced with two dots between each.