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

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\}

using the IQR rule.

Example 4

easy

True or false: the IQR rule uses only

Q_1

Q_3

, and the IQR.

Example 5

medium

Data:

4, 7, 8, 9, 10, 11, 12, 50

. With

Q_1=7.5

and

Q_3=11.5

, use the

1.5\times

IQR rule to identify outliers.

Example 6

hard

A typo records a person's age as

250

instead of

25

. 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\}

. Use the

1.5 \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=2.5

point is an outlier, the other says it is not. Using the common

|z|>3

threshold, who is right, and what does this reveal about outlier rules?

Example 9

medium

Compute the upper fence for

Q_1 = 11

Q_3 = 21

. Is

35

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, 30

. Find

Q_1

Q_3

, the IQR, and use the

1.5\times

IQR rule to list all outliers.

Example 12

medium

Mean

=100

, SD

=10

. Two values are observed:

125

and

108

. Using

|z|>3

, which (if any) is an outlier?

Example 13

hard

Adding the value

1000

to a 10-element data set whose mean is

50

and SD is

5

. 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\}

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, 21

. Should you investigate

200

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

is commonly flagged as an ___.

Example 19

hard

A single value at

z = 5

is found in a sample of

1000

. Should it be deleted automatically?

Example 20

medium

A data set has mean

50

and standard deviation

4

. A value of

66

is observed. Compute its

z

-score and decide whether it's an outlier by the

|z| > 3

rule.

← Back to Outliers (Deep) Worked Examples Formula Explained

Related Concepts

Variability Interquartile Range Box Plot