Quartile vs IQR
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Quartile
Describing data
A quartile is one of three values that divide an ordered data set into four groups of roughly equal size.
Quartiles split ordered data into four parts, marked by the first quartile , the median, and the third quartile . The first quartile is the median of the lower half and the third quartile is the median of the upper half. For example, in 2, 4, 6, 8, 10 the median is 6, so you exclude it and get and . This site uses the median-excluded convention (the TI-84 method), which drops the overall median when the count is odd.
Interquartile range (IQR)
Describing data
The interquartile range (IQR) is the spread of the middle half of the data, equal to the third quartile minus the first quartile.
The interquartile range measures how spread out the middle 50 percent of the data is, so it ignores the extreme quarters. You compute it as , the third quartile minus the first quartile. For example, if and , then the IQR is . Because it drops the top and bottom quarters, the IQR is resistant to outliers and drives the 1.5 times IQR rule for flagging them.