Question

b) find the interquartile range.
c) from this data set, what is the lowest temperature possible that would not be considered an outlier?
d) from this data set, what is the highest number possible that would not be considered an outlier?

Explanation:

Step1: Identify quartiles

From the 5 - number summary \(55,57.5,59.5,62.5,69\), \(Q_1 = 57.5\), \(Q_3=62.5\)

Step2: Calculate inter - quartile range (IQR)

\(IQR=Q_3 - Q_1\)
\(IQR = 62.5-57.5=5\)

Step3: Calculate lower fence (for non - outlier)

Lower fence \(=Q_1-1.5\times IQR\)
\(=57.5 - 1.5\times5\)
\(=57.5-7.5 = 50\)

Step4: Calculate upper fence (for non - outlier)

Upper fence \(=Q_3 + 1.5\times IQR\)
\(=62.5+1.5\times5\)
\(=62.5 + 7.5=70\)

Answer:

c) \(50^{\circ}F\)
d) \(70^{\circ}F\)