What is the IQR and how is it used to identify outliers?

• A. IQR = Q3 - Q1; outliers are below Q1 - 1.5*IQR or above Q3 + 1.5*IQR
• B. IQR = Q3 - Q1; outliers are below Q3 - 1.5*IQR
• C. IQR = mean - median; outliers are below Q1 - 1*IQR
• D. IQR = max - min; outliers outside [Q1, Q3]

Answer: (A)

The IQR measures how spread out the middle half of the data is. It’s calculated as Q3 minus Q1, so it focuses on the central 50% and is less influenced by extreme values.

To flag outliers, we use Tukey’s fences: the lower fence is Q1 minus 1.5 times the IQR, and the upper fence is Q3 plus 1.5 times the IQR. Any value beyond these fences is considered an outlier. This approach captures unusually extreme observations while allowing normal variation in the data.

So the correct idea is that IQR equals Q3 minus Q1 and outliers lie below Q1 minus 1.5 times the IQR or above Q3 plus 1.5 times the IQR. The other statements misstate the definition of IQR or the rule for identifying outliers (for example, using only one fence, using mean–median, or treating the range [Q1, Q3] as the boundary).