Question

1. a set of test scores has the following 5 - number summary: minimum q1 median q3 maximum 2 18 22.5 28.5 33 which statement about outliers must be true? (a) there is exactly one outlier on the lower end. (b) there is at least one outlier on the lower end. (c) there is exactly one outlier on the higher end. (d) there is at least one outlier on the higher end. (e) there are no outliers.

Explanation:

Step1: Calculate the inter - quartile range (IQR).

$IQR = Q3 - Q1$
$IQR=28.5 - 18=10.5$

Step2: Calculate the lower fence.

Lower fence $=Q1 - 1.5\times IQR$
$=18-1.5\times10.5=18 - 15.75 = 2.25$

Step3: Calculate the upper fence.

Upper fence $=Q3 + 1.5\times IQR$
$=28.5+1.5\times10.5=28.5 + 15.75=44.25$

Step4: Analyze the data points.

The minimum value is 2, which is less than the lower fence of 2.25. So, there is at least one outlier on the lower end.

Answer:

B. There is at least one outlier on the lower end.