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? 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.
Answer
Answer:
The greatest value, 78, is the only outlier.
Explanation:
Step1: Calculate the inter - quartile range (IQR)
$IQR = Q_3 - Q_1=37 - 13 = 24$
Step2: Calculate the lower fence
Lower fence $=Q_1-1.5\times IQR=13-1.5\times24=13 - 36=-23$
Step3: Calculate the upper fence
Upper fence $=Q_3 + 1.5\times IQR=37+1.5\times24=37 + 36 = 73$
Step4: Identify outliers
Values less than the lower fence or greater than the upper fence are outliers. The value 78 is greater than 73, so 78 is an outlier. The value 1 is within the range of - 23 to 73, so it is not an outlier.