A survey taken in a large statistics class contained the question: "What's the fastest you have driven a car (in miles per hour)?" The five-number summary for the 87 males surveyed is:min = 55, Q1 = 95, Median = 110, Q3 = 120, Max = 155Should the largest observation in this data set be classified as an outlier?YesNo
Question
A survey taken in a large statistics class contained the question: "What's the fastest you have driven a car (in miles per hour)?" The five-number summary for the 87 males surveyed is:min = 55, Q1 = 95, Median = 110, Q3 = 120, Max = 155Should the largest observation in this data set be classified as an outlier?YesNo
Solution
Based on the given five-number summary for the 87 males surveyed, the largest observation in the data set is 155 miles per hour. To determine if this observation should be classified as an outlier, we can use the interquartile range (IQR) method.
The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). In this case, the IQR is 120 - 95 = 25.
According to the IQR method, any observation that is more than 1.5 times the IQR above the third quartile or below the first quartile can be classified as an outlier.
In this case, 1.5 times the IQR is 1.5 * 25 = 37.5. Adding this value to Q3 gives us 120 + 37.5 = 157.5.
Since the largest observation in the data set (155) is less than 157.5, it is not considered an outlier based on the IQR method.
Therefore, the answer to the question "Should the largest observation in this data set be classified as an outlier?" is No.
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