How is the interquartile range (IQR) defined?

The interquartile range (IQR) is defined specifically as the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. It measures the range within which the central 50% of the data falls, effectively providing insight into the variability or dispersion of the middle half of the data. By focusing on Q1 and Q3, the IQR is not influenced by outliers or extreme values that may skew the overall dataset, making it a robust measure of spread.

In this context, the option that includes both the second and third quartiles correctly captures the essence of the IQR because Q1 is technically the second quartile, considering that quartiles are often labeled based on their positional order within a sorted dataset. Therefore, referencing the second (Q2 which is the median) and third quartiles (Q3) highlights an understanding that the IQR prominently involves the upper and lower quartiles, emphasizing the range defined between these points. This makes it particularly valuable for identifying the middle range of data while excluding the influence of outliers, solidifying the correct choice regarding the definition of the IQR.