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A set of data has the following five number summary: minimum = 17, first quartile = 27, median = 40, third quartile = 49, maximum = 90. Which of the sets of numbers below contain all outliers? Option 1: 60, 70, 80 Option 2: 10, 15, 20 Option 3: 35, 45, 50 Option 4: 80, 85, 90

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2 votes

Answer:

Explanation:

To determine if a set of numbers contains outliers, we need to compare them to the five-number summary of the data: minimum, first quartile, median, third quartile, and maximum.

In this case, the five-number summary is:

Minimum = 17

First quartile = 27

Median = 40

Third quartile = 49

Maximum = 90

To identify outliers, we can use the interquartile range (IQR). The IQR is the difference between the third quartile and the first quartile. In this case, the IQR is 49 - 27 = 22.

According to the Tukey's fences rule, any value below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR is considered an outlier.

Let's evaluate each set of numbers:

Option 1: 60, 70, 80

None of these values are below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. So, option 1 does not contain any outliers.

Option 2: 10, 15, 20

All of these values are below Q1 - 1.5 * IQR. Therefore, option 2 contains outliers.

Option 3: 35, 45, 50

None of these values are below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. So, option 3 does not contain any outliers.

Option 4: 80, 85, 90

All of these values are above Q3 + 1.5 * IQR. Therefore, option 4 contains outliers.

In summary, options 2 and 4 contain outliers, as they have values that are below Q1 - 1.5 * IQR and above Q3 + 1.5 * IQR, respectively.

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