Question

Outliers
Consider the data set: {90, 94, 89, 92, 89, 103, 77, 92, 94, 90}
In the given data set, which should be considered a possible outlier?
A 77 only
B 103 only
C 77 and 103 only
D 77, 97, and 103
If added to the given data set, which would NOT be considered a possible outlier?
A 78
B 80
C 85
D 102
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Answer 1

Use the 1.5·IQR rule.

Sort the data: 77, 89, 89, 90, 90, 92, 92, 94, 94, 103
n = 10 → Q1 = 89, Q3 = 94, IQR = 5
Lower fence = 89 − 1.5(5) = 81.5; Upper fence = 94 + 1.5(5) = 101.5

- Values outside (<81.5 or >101.5) are outliers → 77 and 103 are outliers. Answer to first question: C (77 and 103 only).

If each value is added and quartiles recomputed (n = 11), the fences remain 81.5 and 101.5 in each case above:
- 78, 80, 102 are outside the fences (outliers).
- 85 is inside the fences (not an outlier).

So answer to second question: C (85).