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: Calculate the inter - quartile range (IQR)

$IQR = Q_3 - Q_1$, where $Q_1 = 13$ (lower quartile) and $Q_3=37$ (upper quartile). So, $IQR=37 - 13=24$.

Step2: Calculate the lower and upper bounds for non - outliers

The lower bound for non - outliers is $Q_1-1.5\times IQR$. Substitute the values: $13-1.5\times24=13 - 36=-23$.
The upper bound for non - outliers is $Q_3 + 1.5\times IQR$. Substitute the values: $37+1.5\times24=37 + 36 = 73$.

Step3: Check for outliers

The data set is $1,12,13,15,18,20,35,37,40,78$. The value $1$ is greater than $-23$ and the value $78$ is greater than $73$. So, $78$ is an outlier and $1$ is not an outlier.

Answer:

The greatest value, 78, is the only outlier.