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 $Q_1 = 13$ and $Q_3 = 37$. So, $IQR=37 - 13=24$.

Step2: Calculate the lower fence

Lower fence $=Q_1-1.5\times IQR$. Substitute the values: $13-1.5\times24=13 - 36=-23$.

Step3: Calculate the upper fence

Upper fence $=Q_3 + 1.5\times IQR$. Substitute the values: $37+1.5\times24=37 + 36 = 73$.

Step4: Check for outliers

Values less than the lower fence or greater than the upper fence are outliers. The lower fence is - 23 and the upper fence is 73. The value 78 is greater than 73, so 78 is an outlier. The value 1 is within the range of - 23 to 73, so 1 is not an outlier.

Answer:

The greatest value, 78, is the only outlier.