How do you compare data sets using interquartile range?

You compare data sets using interquartile range (IQR) by measuring the spread of the middle 50% of the data.

The interquartile range (IQR) is a measure of statistical dispersion, or how spread out the values in a data set are. To find the IQR, you first need to determine the first quartile (Q1) and the third quartile (Q3) of the data set. The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half. The IQR is then calculated by subtracting Q1 from Q3 (IQR = Q3 - Q1).

When comparing two or more data sets, the IQR helps you understand the variability within each set. A larger IQR indicates that the data is more spread out, while a smaller IQR suggests that the data is more clustered around the median. For example, if Data Set A has an IQR of 10 and Data Set B has an IQR of 5, Data Set A has more variability in its middle 50% of values compared to Data Set B.

Using the IQR is particularly useful because it is not affected by outliers or extreme values, which can skew other measures of spread like the range. This makes the IQR a robust measure for comparing the consistency and reliability of different data sets. By analysing the IQR, you can gain insights into the distribution and spread of the data, helping you make more informed decisions based on the data's characteristics.