Question

1. a data set has q1 = 12, q3 = 30, and an iqr of 18. which value would be considered an outlier?

a. 32
b. 10
c. 20
d. 60

Explanation:

Step1: Recall outlier formula

Lower bound: \( Q1 - 1.5 \times IQR \)
Upper bound: \( Q3 + 1.5 \times IQR \)

Step2: Calculate lower bound

\( Q1 = 12 \), \( IQR = 18 \)
Lower bound: \( 12 - 1.5 \times 18 = 12 - 27 = -15 \)

Step3: Calculate upper bound

\( Q3 = 30 \), \( IQR = 18 \)
Upper bound: \( 30 + 1.5 \times 18 = 30 + 27 = 57 \)

Step4: Check each option

• a. 32: \( -15 < 32 < 57 \) (not outlier)
• b. 10: \( -15 < 10 < 57 \) (not outlier)
• c. 20: \( -15 < 20 < 57 \) (not outlier)
• d. 60: \( 60 > 57 \) (outlier)

Answer:

d. 60