Question

the data set below has a lower quartile of 13 and an upper quartile of 37. 1, 12, 13, 15, 18, 20, 35, 37, 40, 78. which statement is true about any outliers of the data set? the data set does not have any outliers. the lowest value, 1, is the only outlier. the greatest value, 78, is the only outlier. both 1 and 78 are outliers.

Explanation:

Step1: Recall outlier formula

Outliers are values less than $Q_1 - 1.5\times IQR$ or greater than $Q_3+ 1.5\times IQR$, where $IQR = Q_3 - Q_1$. Given $Q_1 = 13$ and $Q_3=37$, then $IQR=37 - 13=24$.

Step2: Calculate lower - bound for outliers

$Q_1-1.5\times IQR=13-1.5\times24=13 - 36=- 23$.

Step3: Calculate upper - bound for outliers

$Q_3 + 1.5\times IQR=37+1.5\times24=37 + 36 = 73$.

Step4: Identify outliers

The data set is 1, 12, 13, 15, 18, 20, 35, 37, 40, 78. The value 78 is greater than 73, and the value 1 is less than - 23. So both 1 and 78 are outliers.

Answer:

Both 1 and 78 are outliers.