Question

the five - number summary of a data set is given below. minimum: 3 q1: 12 median: 15 q3: 16 maximum: 20 which of the following is a true statement about outliers for this distribution? the distributions maximum is an outlier. the distributions minimum is an outlier. there are no outliers for this distribution. distribution outliers cannot be determined.

Explanation:

Step1: Calculate the inter - quartile range (IQR)

$IQR = Q_3 - Q_1=16 - 12 = 4$

Step2: Calculate the lower fence

Lower fence $=Q_1-1.5\times IQR=12-1.5\times4=12 - 6 = 6$

Step3: Calculate the upper fence

Upper fence $=Q_3 + 1.5\times IQR=16+1.5\times4=16 + 6 = 22$

Step4: Check for outliers

The minimum value is 3, which is less than the lower fence of 6. The maximum value is 20, which is less than the upper fence of 22.

Answer:

The distribution's minimum is an outlier.