Question

the 10 members of the swim team completed the following numbers of laps at todays practice. 29, 77, 78, 83, 87, 89, 90, 92, 92, 156 identify all values that are outliers. if there is more than one outlier, separate them with commas. if there are no outliers, click on
one\.

Explanation:

Step1: Sort the data

First, sort the data set \(29,77,78,83,87,89,90,92,92,156\) in ascending order: \(29,77,78,83,87,89,90,92,92,156\).

Step2: Find the first quartile \(Q_1\)

The first quartile \(Q_1\) is the median of the lower half of the data. The lower half is \(29,77,78,83,87\). The median of this set is \(78\).

Step3: Find the third quartile \(Q_3\)

The third quartile \(Q_3\) is the median of the upper half of the data. The upper half is \(89,90,92,92,156\). The median of this set is \(92\).

Step4: Calculate the inter - quartile range \(IQR\)

The inter - quartile range \(IQR=Q_3 - Q_1\). So \(IQR = 92-78=14\).

Step5: Determine the lower and upper bounds for outliers

The lower bound for outliers is \(Q_1-1.5\times IQR\). \(78-1.5\times14=78 - 21=57\).
The upper bound for outliers is \(Q_3 + 1.5\times IQR\). \(92+1.5\times14=92+21 = 113\).

Step6: Identify outliers

Any value less than \(57\) or greater than \(113\) is an outlier. In the data set, \(29<57\) and \(156>113\).

Answer:

\(29,156\)