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)

The formula for IQR is $IQR = Q_3 - Q_1$, where $Q_1$ is the lower quartile and $Q_3$ is the upper quartile. Given $Q_1 = 13$ and $Q_3=37$, so $IQR=37 - 13=24$.

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

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

Step3: Check for outliers

Any value less than the lower bound or greater than the upper bound is an outlier. 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.