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).

$IQR = Q_3 - Q_1=37 - 13 = 24$

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.

The data 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 (-23, 73), so 1 is not an outlier.

Answer:

The greatest value, 78, is the only outlier.