Question

a random sample of sale prices of homes yielded the following summary information. min $46,000 25%: $85,000 median: $125,000 max $273,000 75%: $165,000 comment on a home that had a sale price of $412,000. a. this sale price would be expected since it falls inside the lower and upper fences. b. this sale price falls between the lower and upper fences. it can be considered a potential outlier. c. this value falls outside the upper fence and is considered an outlier. d. this value falls outside of the third quartile, but cannot be considered an outlier.

Explanation:

Step1: Calculate the inter - quartile range (IQR)

The inter - quartile range \(IQR = Q_{3}-Q_{1}\). Given \(Q_{1} = 85000\) and \(Q_{3}=165000\), then \(IQR=165000 - 85000=80000\)

Step2: Calculate the upper fence

The upper fence is \(Q_{3}+1.5\times IQR\). Substitute \(Q_{3}=165000\) and \(IQR = 80000\) into the formula: \(165000+1.5\times80000=165000 + 120000=285000\)

Step3: Compare the value with the upper fence

The value of the sale price is \(x = 412000\). Since \(412000>285000\)

Answer:

C. This value falls outside the upper fence and is considered an outlier.