Quartiles and interquartile range belong to the position measures. As the name suggests, quartiles divide a ranked record (ordered set of data) into four equal parts. It only takes three steps to break a data set into four equal parts.
These three measures, which divide an ordered data set into four equal parts, are the first quartile (labeled Q1), the second quartile (denoted by Q2) and the third quartile (denoted by Q3rd).
After a record has been ordered or written in ascending order, we define the quartiles as follows.
The second quartile, or Q2is equal to the median of the data set after the data set was ordered.
The first quartile or Q1 is the median between the smallest number and the second quartile.
The third quartile, or Q3rd is the median between the second quartile and the largest number.
Now look at the following illustration, and then make the following key observations.
- About 25% of the values in the ordered data set are less than Q1
- You can also say that about 75% of the values in the ordered record are greater than Q. are1
- Approximately 75% of the values in the ordered data set are less than Q3rd
- You could also say that about 25% of the values in the ordered dataset are greater than Q. are3rd
- About 50% of the values in the ordered data set are smaller than Q2 and about 50% are larger than Q2
The interquartile range is the difference between the third quartile and the first quartile.
IQR = interquartile range = Q3rd – Q1