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 Q_{1}), the second quartile (denoted by Q_{2}) and the third quartile (denoted by Q_{3rd}).

After a record has been ordered or written in ascending order, we define the quartiles as follows.

The second quartile, or Q_{2}_{}is equal to the median of the data set after the data set was ordered.

The first quartile or Q_{1 }is the median between the smallest number and the second quartile.

The third quartile, or Q_{3rd} 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 Q
_{1 }

- You can also say that about 75% of the values in the ordered record are greater than Q. are
_{1}

- Approximately 75% of the values in the ordered data set are less than Q
_{3rd}

- You could also say that about 25% of the values in the ordered dataset are greater than Q. are
_{3rd}

- About 50% of the values in the ordered data set are smaller than Q
_{2}and about 50% are larger than Q_{2}

## Interquartile range

The interquartile range is the difference between the third quartile and the first quartile.

IQR = interquartile range = Q_{3rd }– Q_{1}