Question

the test scores for a group of students are shown. (same data set from the previous question)
60, 69, 79, 80, 86, 86, 86, 89, 90, 100
which test score is an outlier?
i dont know
69
90
60
100

Explanation:

Step1: Arrange data in order

The data is already in ascending - order: 60, 69, 79, 80, 86, 86, 86, 89, 90, 100.

Step2: Find the median (Q2)

There are \(n = 10\) data - points. The median is the average of the 5th and 6th ordered values. So, \(Q2=\frac{86 + 86}{2}=86\).

Step3: Find the lower half and Q1

The lower half of the data is 60, 69, 79, 80, 86. The median of the lower half (\(Q1\)) is the 3rd value, so \(Q1 = 79\).

Step4: Find the upper half and Q3

The upper half of the data is 86, 89, 90, 100. The median of the upper half (\(Q3\)) is the 3rd value of the upper - half, so \(Q3=90\).

Step5: Calculate the inter - quartile range (IQR)

\(IQR=Q3 - Q1=90 - 79 = 11\).

Step6: Determine the outlier boundaries

Lower boundary \(=Q1-1.5\times IQR=79-1.5\times11=79 - 16.5 = 62.5\).
Upper boundary \(=Q3 + 1.5\times IQR=90+1.5\times11=90 + 16.5 = 106.5\).

Step7: Identify the outlier

Any value less than 62.5 or greater than 106.5 is an outlier. The value 60 is less than 62.5, so 60 is an outlier.

Answer:

D. 60