Practice Outliers (Deep) in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

An outlier is a data value that lies unusually far from most other values, potentially indicating measurement error, a rare event, or an important exception.

The weird one that doesn't fit. Is it a mistake, or something interesting?

Showing a random 20 of 50 problems.

Example 1

easy
Which boxplot feature shows where outliers are located?

Example 2

hard
Compare the IQR rule to the ∣z∣>3|z| > 3 rule. When does the z-score rule fail?

Example 3

medium
Find all outliers in {1,2,3,4,5,6,7,8,9,50}\{1, 2, 3, 4, 5, 6, 7, 8, 9, 50\} using the IQR rule.

Example 4

easy
True or false: the IQR rule uses only Q1Q_1, Q3Q_3, and the IQR.

Example 5

medium
Data: 4,7,8,9,10,11,12,504, 7, 8, 9, 10, 11, 12, 50. With Q1=7.5Q_1=7.5 and Q3=11.5Q_3=11.5, use the 1.5×1.5\timesIQR rule to identify outliers.

Example 6

hard
A typo records a person's age as 250250 instead of 2525. Why might this be a worse problem for the mean than for the median?

Example 7

medium
Data: {12,15,14,13,16,14,15,85}\{12, 15, 14, 13, 16, 14, 15, 85\}. Use the 1.5×IQR1.5 \times IQR rule to determine if 85 is an outlier, and discuss whether it should be removed.

Example 8

challenge
Two analysts disagree: one says a z=2.5z=2.5 point is an outlier, the other says it is not. Using the common ∣z∣>3|z|>3 threshold, who is right, and what does this reveal about outlier rules?

Example 9

medium
Compute the upper fence for Q1=11Q_1 = 11, Q3=21Q_3 = 21. Is 3535 an outlier?

Example 10

easy
True or false: every outlier is a data-entry error that should be deleted.

Example 11

challenge
Data: 1,2,2,3,3,3,4,4,5,301, 2, 2, 3, 3, 3, 4, 4, 5, 30. Find Q1Q_1, Q3Q_3, the IQR, and use the 1.5×1.5\timesIQR rule to list all outliers.

Example 12

medium
Mean =100=100, SD =10=10. Two values are observed: 125125 and 108108. Using ∣z∣>3|z|>3, which (if any) is an outlier?

Example 13

hard
Adding the value 10001000 to a 10-element data set whose mean is 5050 and SD is 55. Roughly, what happens to the SD?

Example 14

easy
Does an outlier affect the mean or the median more?

Example 15

hard
For {1,2,2,3,3,3,4,4,5}\{1, 2, 2, 3, 3, 3, 4, 4, 5\} identify the IQR fences and any outliers.

Example 16

easy
A class scores mostly 70–90, but one student scored 5 by leaving the test blank. Is this outlier likely an error or a real value?

Example 17

medium
A sensor logs 20,21,19,20,200,2120, 21, 19, 20, 200, 21. Should you investigate 200200 before deciding it is a glitch, and what is the robust center estimate?

Example 18

easy
Fill in the blank: A value with ∣z∣>3|z| > 3 is commonly flagged as an ___.

Example 19

hard
A single value at z=5z = 5 is found in a sample of 10001000. Should it be deleted automatically?

Example 20

medium
A data set has mean 5050 and standard deviation 44. A value of 6666 is observed. Compute its zz-score and decide whether it's an outlier by the ∣z∣>3|z| > 3 rule.
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