Question

a survey taken of 140 sports fans asked the question: what is the most you have ever spent for a ticket to a sporting event? the five - number summary for the data collected is: min = 85, q1 = 130, median = 145, q3 = 150, max = 250. is the smallest observation an outlier? yes no

Explanation:

Step1: Calculate IQR

IQR (Interquartile Range) is calculated as \( Q3 - Q1 \). Given \( Q1 = 130 \) and \( Q3 = 150 \), so \( IQR = 150 - 130 = 20 \).

Step2: Calculate Lower Fence

The lower fence for outliers is calculated as \( Q1 - 1.5 \times IQR \). Substituting the values, we get \( 130 - 1.5 \times 20 = 130 - 30 = 100 \).

Step3: Compare Minimum with Lower Fence

The minimum value (min) is 85. Since \( 85 < 100 \) (the lower fence), the smallest observation is an outlier.

Answer:

Yes