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 = 155 Should the largest observation in this data set be classified as an outlier? No Yes

Question

Mathematics

Sydney Sutton

31 August, 02:16

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 = 155 Should the largest observation in this data set be classified as an outlier? No Yes

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Answers (1)

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Karen Oconnor · Answer 1

NO

Step-by-step explanation:

To find out which observation to classify as an outlier, whether the largest or not, a very good approach or way to do this is to apply the 1.5 (IQR) rule.

According to the rule, for finding the largest observation in the data that can be classified as an outlier, we would use the formula = Q3 + 1.5 (IQR).

Q3 = 120

IQR = Q3 - Q1 = 120 - 95 = 25

Lets's plug these values into Q3 + 1.5 (IQR)

We have,

120 + 1.5 (25)

= 157.5

Since our max in the observation is given as 155, the largest observation in the data set cannot be set as an outlier because 157.5 which we got from our calculation is higher than the max value we have in the data set.

Our answer is NO.

However, the smallest observation should be set as outlier because:

Q1 - 1.5 (IQR) = 95 - (1.5*25) = 57.5, which gives us an outlier that falls within our data range.