QUESTION 14 - I POINT The five number summary for a set of data is given below. \begin{tabular}{ccccc} Min & Q1 & Median & Q3 & Max \\ \hline 40 & 69 & 72 & 79 & 86 \end{tabular} Using the interquartile range, which of the following are outliers? Select all correct answers. Select all that apply: 43 44 48 64 70
Solution
Step 1 ：First, let's calculate the interquartile range (IQR). The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). In this case, Q3 is 79 and Q1 is 69. So, the IQR is \(79 - 69 = 10\).
Step 2 ：Next, let's calculate the lower and upper bounds for outliers. Any number that falls below \(Q1 - 1.5*IQR\) or above \(Q3 + 1.5*IQR\) is considered an outlier. The lower bound is \(69 - 1.5*10 = 54\) and the upper bound is \(79 + 1.5*10 = 94\).
Step 3 ：Finally, let's check which numbers from the given options are outliers. The options are 43, 44, 48, 64, and 70. The numbers 43, 44, and 48 are below the lower bound, so they are outliers. The numbers 64 and 70 are within the bounds, so they are not outliers.
Step 4 ：The outliers are \(\boxed{43, 44, 48}\).
