Question

which of the following statements is true? remember: outliers are 1.5 iqrs greater than the upper quartile or 1.5 iqrs less than the lower quartile. a the player with a height of 72 inches is an outlier to the data set represented. b no player has a height that is considered an outlier to the data set represented. c the player with a height of 86 inches is an outlier to the data set represented.

Explanation:

Step1: Recall outlier rule

Outliers are values that are 1.5 IQRs (inter - quartile ranges) greater than the upper quartile ($Q_3$) or 1.5 IQRs less than the lower quartile ($Q_1$). Without information about $Q_1$, $Q_3$ and IQR of the data - set of player heights, we assume we need to check each option against the rule.

Step2: Analyze option A

We don't know if 72 inches is 1.5 IQRs less than $Q_1$ or 1.5 IQRs greater than $Q_3$. So we can't say it's an outlier.

Step3: Analyze option B

We don't have enough information to conclude that no player is an outlier.

Step4: Analyze option C

We don't know if 86 inches is 1.5 IQRs less than $Q_1$ or 1.5 IQRs greater than $Q_3$. So we can't say it's an outlier.
However, if we assume a normal - range of human heights for basketball players (for example, if the typical range is between say 65 - 80 inches), 86 inches is likely to be greater than $Q_3+ 1.5IQR$. But this is an assumption. If we go by the strict rule and no other data about the quartiles and IQR, we can't be sure. But if we had to choose based on general knowledge of height data for such cases, 86 inches is more likely to be an outlier.

Answer:

C. The player with a height of 86 inches is an outlier to the data set represented.