Question

identify all values, if any, in the data set that would be considered outliers when creating a modified boxplot. 71 74 78 79 79 80 82 (1 point) o 71 o 82 o 71 and 82 o no outliers

Explanation:

Step1: Find median ($Q_2$)

The data set is \(71,74,78,79,79,80,82\). Since \(n = 7\) (odd), \(Q_2=79\).

Step2: Find lower half and \(Q_1\)

Lower half: \(71,74,78\). \(Q_1 = 74\).

Step3: Find upper half and \(Q_3\)

Upper half: \(79,80,82\). \(Q_3 = 80\).

Step4: Calculate \(IQR\)

\(IQR=Q_3 - Q_1=80 - 74 = 6\).

Step5: Find lower and upper fences

Lower fence: \(Q_1-1.5\times IQR=74-1.5\times6=74 - 9=65\).
Upper fence: \(Q_3 + 1.5\times IQR=80+1.5\times6=80 + 9=89\).

Step6: Check for outliers

All data values (\(71,74,78,79,79,80,82\)) are between \(65\) and \(89\).

Answer:

no outliers