Question

which data values of the following set are outliers? 32, 38, 38, 40, 42, 44, 46, 48, 49, 60, 72 remember: outliers are 1.5 iqrs less than the lower boundary or 1.5 iqrs greater than the upper boundary. a there are no outliers in the data set. b 72 c 32

Explanation:

Step1: Find the median

The data set has 11 values. The median (Q2) is the 6th - ordered value, so Q2 = 44.

Step2: Find Q1 and Q3

The lower - half of the data set is 32, 38, 38, 40, 42. The median of the lower - half (Q1) is 38. The upper - half of the data set is 46, 48, 49, 60, 72. The median of the upper - half (Q3) is 49.

Step3: Calculate the IQR

IQR=Q3 - Q1 = 49 - 38=11.

Step4: Calculate the lower and upper boundaries

The lower boundary is Q1−1.5×IQR = 38−1.5×11=38 - 16.5 = 21.5. The upper boundary is Q3 + 1.5×IQR=49+1.5×11=49 + 16.5 = 65.5.

Step5: Identify outliers

Values less than 21.5 or greater than 65.5 are outliers. In the data set, 72>65.5, so 72 is an outlier.

Answer:

B. 72