QQuestionMathematics
QuestionMathematics
The " $1.5 \times$ IQR" rule states that a data value is potentially an outlier if its distance below the first quartile or above the third quartile is greater than 1.5 times the interquartile range. Which of the following box plots represents a data set with a potential outlier, as identified by the " $1.5 \times$ IQR" rule? Select all that apply.
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Answer
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Step 1:: Identify the box plots with potential outliers based on the " $1.5 imes$ IQR" rule.
The " $1.5 imes$ IQR" rule states that a data value is potentially an outlier if its distance below the first quartile (Q1) or above the third quartile (Q3) is greater than 1.5 times the interquartile range (IQR = Q3 - Q1).
To apply this rule, we first need to identify Q^1, Q^3, and the IQR for each box plot.
Step 2:: Analyze the first box plot.
In the first box plot, the upper edge of the box is around 8, and the line extending from the box (whisker) reaches approximately 10. The lower edge of the box is around 2, and the lower whisker reaches approximately 0. Here, Q^1 is around 2, Q^3 is around 8, and IQR = Q^3 - Q^1 = 8 - 2 = 6.
Step 3:: Check for potential outliers in the first box plot.
Therefore, there are no potential outliers in the first box plot according to the " $1.5 imes$ IQR" rule.
Since the upper whisker reaches approximately 10, there are no data values above this limit.
Step 4:: Analyze the second box plot.
In the second box plot, the upper edge of the box is around 7, and the whisker reaches approximately 12. The lower edge of the box is around 1, and the lower whisker reaches approximately - 3. Here, Q^1 is around 1, Q^3 is around 7, and IQR = Q^3 - Q^1 = 7 - 1 = 6.
Step 5:: Check for potential outliers in the second box plot.
The upper limit for data values to not be considered outliers is Q3 + 1.5 $\times$ IQR = 7 + 1.5 $\times$ 6 = 15.5.
The data value 12 is above this limit, so it is a potential outlier.
Step 6:: Analyze the third box plot.
In the third box plot, the upper edge of the box is around 6, and the whisker reaches approximately 9.5. The lower edge of the box is around 1.5, and the lower whisker reaches approximately - 1.5. Here, Q^1 is around 1.5, Q^3 is around 6, and IQR = Q^3 - Q^1 = 6 - 1.5 = 4.5.
Step 7:: Check for potential outliers in the third box plot.
The data value 9.5 is below this limit, so there are no potential outliers in the third box plot according to the " $1.5 imes$ IQR" rule.
Final Answer
The box plots with potential outliers, as identified by the " $1.5 imes$ IQR" rule, are the second and fourth box plots.
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