Final answer:
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset, reflecting the spread of the middle 50% of the data. In a data set with Q1 = 2 and Q3 = 9, the IQR would be 7. The IQR is used to identify potential outliers in the data set.
Step-by-step explanation:
The interquartile range (IQR) is a measure of statistical dispersion and is calculated as the difference between the third and first quartiles (Q3 - Q1). To interpret the IQR, consider it as the range of the middle 50% of the data points in a dataset. Using a simple numerical example, if the data set's Q1 is 2 and Q3 is 9, then the IQR is calculated as 9 minus 2, resulting in an IQR of 7.
An important application of the IQR is in identifying potential outliers. An outlier is a data point that is significantly distant from the rest of the data. A data point is considered a potential outlier if it is less than Q1 - 1.5 × IQR or more than Q3 + 1.5 × IQR. Outliers should be investigated as they can indicate data entry errors, measurement errors, or they could be valid but unusual points that may be of particular interest.