What is the Interquartile Range?

The Interquartile Range (IQR) is a statistical measure that is used to identify the dispersion or spread of a data set. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Here are the steps to calculate it:

1. Arrange the data in increasing order.

2. Find the median of the data set. This is also known as the second quartile (Q2).

3. Divide the data set into two halves: the lower half and the upper half. The lower half is the set of all values that are less than the median, and the upper half is the set of all values that are greater than the median.

4. Find the median of the lower half. This is the first quartile (Q1).

5. Find the median of the upper half. This is the third quartile (Q3).

6. Subtract Q1 from Q3 to get the Interquartile Range (IQR).

The IQR is a measure of variability, based on dividing a data set into quartiles. Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively.

Q1 is the "middle" value in the first half of the rank-ordered data set. Q2 is the median value in the set. Q3 is the "middle" value in the second half of the rank-ordered data set.

The interquartile range is equal to Q3 minus Q1.