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

Question

BlackTom AI · Accepted Answer

Starting with the concept of outliers in a boxplot, we look at the common rule based on the interquartile range (IQR). The IQR is the distance between the first quartile (Q1) and the third quartile (Q3). In the boxplot shown, the lower edge of the box is around 60 and the upper edge is around 65, which suggests Q1 ≈ 60 and Q3 ≈ 65. The IQR is therefore roughly 65 − 60 = 5.

Next, the typical outlier cutoff uses 1.5 times the IQR beyond the quartiles. Compute the lower fence as Q1 − 1.5 × IQR = 60 − 1.5 × 5 = 60 − 7.5 = 52.5. Compute the upper fence as Q3 + 1.5 × IQR = 65 + 1.5 × 5 = 65 + 7.5 = 72.5.

Thus, any data point below 52.5 or above 72.5 is considered an outlier according to the standard 1.5×IQR rule. Now evaluate the given option(s).

Option: "c. either less than 52.5 or greater than 72.5" — This matches exactly the computed lower and upper fences and correctly identifies outliers as those values beyond these bounds. The logic hinges on applying the IQR rule consistently, which is the conventional method used for boxplots.

If there were other options, we would compare them to the same principle: options that claim outliers are defined by any different thresholds (e.g., based on standard deviation alone, or using the whiskers) would be incorrect under the standard boxplot convention shown here, since the boxplot convention uses the 1.5×IQR rule rather than standard deviation or alternative cutoffs.

In summary, the criterion for being an outlier in this boxplot is a score below 52.5 or above 72.5, which aligns with option c.

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

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

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

The five-number summary for the ages of the attendees at the Pawnee Harvest Festival is listed below. 1 20 29 38 80 I. There is at least one attendee whose age is a low potential outlier. II. There is at least one attendee whose age is a high potential outlier.

How many potential outliers are in the data?

Based on our in-class discussion, which of the following is not a potential cause of outliers?

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