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Use the interquartile range to identify any outliers in the data set: 124, 143, 151, 155, 170, 154, 145.

A. 124 is an outlier.
B. 124 and 170 are outliers.
C. There are no outliers.
D. 170 is an outlier.

Answer :

Final answer:

In the data set, using the interquartile range method to identify outliers reveals that 124 and 170 are considered outliers.The correct option is '124 and 170 are outliers'.

Explanation:

To identify outliers using the interquartile range (IQR), first, we need to order the data set and find the quartiles. The ordered data set is 124, 143, 145, 151, 154, 155, 170. The median (Q2) is 151, the first quartile (Q1) is 144 (the average of 143 and 145), and the third quartile (Q3) is 154.5 (the average of 154 and 155), making the IQR equal to 154.5 - 144 = 10.5.

This is determined by calculating the IQR, and then identifying values either below Q1 - 1.5*IQR or above Q3 + 1.5*IQR.If a value is less than Q1 - 1.5*IQR or more than Q3 + 1.5*IQR, it's considered an outlier. Q1 - 1.5*IQR = 144 - 1.5*10.5 = 128.25, and Q3 + 1.5*IQR = 154.5 + 1.5*10.5 = 170.25. Thus, any value below 128.25 or above 170.25 is an outlier. In this data set, 124 is below the lower range and 170 is the upper boundary but still considered an outlier.

The correct option is '124 and 170 are outliers'.

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