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 = 250Should the smallest observation be classified as an outlier?YesNo
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 = 250Should the smallest observation be classified as an outlier?YesNo
Solution
To determine if the smallest observation should be classified as an outlier, we can use the interquartile range (IQR) method.
Step 1: Calculate the IQR. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). IQR = Q3 - Q1 = 150 - 130 = 20.
Step 2: Calculate the lower fence. The lower fence is calculated by subtracting 1.5 times the IQR from the first quartile. Lower fence = Q1 - (1.5 * IQR) = 130 - (1.5 * 20) = 130 - 30 = 100.
Step 3: Compare the smallest observation to the lower fence. The smallest observation is 85, and the lower fence is 100.
Since the smallest observation (85) is less than the lower fence (100), it can be classified as an outlier. Therefore, the answer is "Yes".
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