To be an outlier in the boxplot above, a score must be:

Question

BlackTom AI · Accepted Answer

The question asks: To be an outlier in the boxplot above, a score must be:

Option analyzed: 'a. either less than 52.5 or greater than 72.5'

First, recall how boxplots define outliers. Outliers are typically identified using the 1.5 IQR rule: any data point below Q1 - 1.5*IQR or above Q3 + 1.5*IQR is an outlier. The boxplot gives us Q1, Q3, and the range of the whiskers, from which we can infer the IQR and the fences.

From the diagram, approximate quartiles appear to be Q1 ≈ 60 and Q3 ≈ 65. Therefore, IQR = Q3 - Q1 ≈ 5. Then 1.5*IQR ≈ 7.5. The lower fence is Q1 - 1.5*IQR ≈ 60 - 7.5 ≈ 52.5, and the upper fence is Q3 + 1.5*IQR ≈ 65 + 7.5 ≈ 72.5. Any score below 52.5 or above 72.5 would be considered an outlier.

Why this makes option a correct: It matches the calculated outlier boundaries (52.5 and 72.5) derived from the 1.5*IQR rule given the approximate quartiles from the box. It correctly identifies the regions outside the whiskers where outliers would lie.

Why other possibilities would be incorrect: Since there are no other options provided here, there isn’t an alternative statement to evaluate. If another option claimed a different boundary (e.g., using a different multiplier or using a different outlier rule), that would not align with the standard 1.5*IQR criterion shown by this boxplot, and would be incorrect given the typical interpretation of boxplots.

In summary, the allowed outlier values are those less than about 52.5 or greater than about 72.5, which is exactly what option a states.

To be an outlier in the boxplot above, a score must be:

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