Question

The five number summary for a set of data is given below.

Min Q1 Median Q3 Max
40 69 72 79 86
Using the interquartile range, which of the following are outliers? Select all correct answers.
Select all that apply:
a.) 43
b.) 44
c.) 48
d.) 64
e.) 70

Answer 1

Outliers in the given dataset are data points 43, 44, and 48, as they are below the lower bound of the interquartile range cutoff, which is 54 in this case. The outliers in the presented options are data points a), b), and c).

Step-by-step explanation:

The student's question pertains to identifying outliers from a set of data using the interquartile range (IQR). Given the five number summary (Min, Q1, Median, Q3, Max), one can calculate the IQR and then determine the cutoff points for outliers. In this case, the IQR is Q3 - Q1, which is 79 - 69 = 10. To identify outliers, we generally look for data points that are more than 1.5 times the IQR above the third quartile or below the first quartile. These are the typical cutoff values for outliers in a dataset.

The cutoff for the lower bound is Q1 - 1.5*IQR = 69 - 1.5*10 = 54. The cutoff for the upper bound is Q3 + 1.5*IQR = 79 + 1.5*10 = 94. Hence, any data points below 54 or above 94 would be considered outliers.

Given this information, the values presented as options in the question can now be assessed:

• 43 - Outlier, as it is less than 54
• 44 - Outlier, as it is less than 54
• 48 - Outlier, as it is less than 54
• 64 - Not an outlier, as it is greater than 54
• 70 - Not an outlier, as it is within the Q1-Q3 range

In conclusion, the outliers in the presented options are data points a), b), and c).