Question

The five-number summary of the ages of passengers on a cruise ship is listed below. Min 1 Q1 20Median 29 Q3 38Max 80 Consider the following two statements regarding outliers for this data and determine which, if any, are correct (i) There is at least one passenger whose age is a low outlier. (ii) There is at least one passenger whose age is a high outlier.a. Only statement (i) is correct. b. Only statement (ii) is correct. c. Both statements (i) and (ii) are correct. d. Neither statement (i) or (ii) is correct.

Answer 1

Answer: b. Only statement (ii) is correct.

Step-by-step explanation:

The given five-number summary of the ages of passengers on a cruise ship is listed below.

Min 1    $Q_1$ 20     Median 29     $Q_3$ 38         Max 80

Inter-quartile range = $IQR=Q_3-Q_1=38-20=18$

• According to the 1.5(IQR) criterion for outliers : An data value is an outlier if it lies below $Q_1 - 1.5(IQR)$ or  above $Q_3 + 1.5(IQR)$.

Here , $Q_1 - 1.5(IQR) =20-1.5(18)=-7$

$Q_3 + 1.5(IQR)=38+1.5(18)=65$

Since the minimum value> $Q_1 - 1.5(IQR)$ ( ∵ 1 > -7)

It means there is no value below $Q_1 - 1.5(IQR)$  , so there is no low -outlier.

⇒ Statement (i) "here is at least one passenger whose age is a low outlier. " is false.

But the maximum value > $Q_3 + 1.5(IQR)$ (∵  85 > 65)

It means there are values above $Q_3 + 1.5(IQR)$.

⇒Statement (ii) "There is at least one passenger whose age is a high outlier" is true.

Hence, the correct answer is b. Only statement (ii) is correct.