Question

1. if the iqr of a data set is 24, which of the following could be the lower bound for outliers?

a. $q1 - 36$
b. $q1 - 15$
c. $q1 - 1.5\times24$
d. $q3 - 24\times1.5$

Explanation:

Step1: Recall the outlier formula

The formula for the lower bound of outliers in a data set is \( \text{Lower Bound} = Q1 - 1.5 \times \text{IQR} \).

Step2: Substitute the given IQR

Given that the IQR is 24, we substitute this into the formula. So the lower bound should be \( Q1 - 1.5\times24 \).

Step3: Analyze the options

• Option a: \( Q1 - 36 \) is incorrect as \( 1.5\times24 = 36 \), but the formula is based on \( Q1 - 1.5\times\text{IQR} \), not just \( Q1 - 36 \) without the context of IQR.
• Option b: \( Q1 - 15 \) does not follow the outlier formula.
• Option c: \( Q1 - 1.5\times24 \) follows the correct formula for the lower bound of outliers.
• Option d: \( Q3 - 24\times1.5 \) is related to the upper bound or incorrect as it uses \( Q3 \) instead of \( Q1 \) for the lower bound.

Answer:

c. \( Q1 - 1.5\times24 \)