the data set below has a lower quartile of 13 and an upper quartile of 37. 1, 12, 13, 15, 18, 20, 35, 37…

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? o the data set does not have any outliers. o the lowest value, 1, is the only outlier. o the greatest value, 78, is the only outlier. o both 1 and 78 are outliers.

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? o the data set does not have any outliers. o the lowest value, 1, is the only outlier. o the greatest value, 78, is the only outlier. o both 1 and 78 are outliers.

Answer

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 $Q_1-1.5\times IQR$. So, $13-1.5\times24=13 - 36=-23$. The upper bound for non - outliers is $Q_3 + 1.5\times IQR$. So, $37+1.5\times24=37 + 36 = 73$.

Step3: Check for outliers

The data values are 1, 12, 13, 15, 18, 20, 35, 37, 40, 78. Since $1>-23$ and $78>73$, 78 is an outlier and 1 is not an outlier.

Answer:

The greatest value, 78, is the only outlier.