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.