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AP Statistics : How to find outliers

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Example Questions

Example Question #1 : How To Find Outliers

Use the following five number summary to determine if there are any outliers in the data set:

Minimum:

Q1:

Median:

Q3:

Maximum:

Possible Answers:

There are no outliers.

There is at least one outlier on the low end of the distribution and no outliers on the high end of the distribution.

There is at least one outlier on the high end of the distribution and no outliers on the low end of the distribution.

It is not possible to determine if there are outliers based on the information given.

There is at least one outlier on the high end of the distribution and at least one outlier on the low end of the distribution.

Correct answer:

There are no outliers.

Explanation:

An observation is an outlier if it falls more than 1.5(IQR) above the upper quartile or more than below the lower quartile.

IQR= Q3-Q1= 12-6=6

1.5(IQR)= 11..5(6)= 9

Q1-9= 6-9= -3 . The minimum value is so there are no outliers in the low end of the distribution.

Q3+9= 12+9= 21 . The maximum value is so there are no outliers in the high end of the distribution.

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Example Question #61 : Data

For a data set, the first quartile is , the third quartile is and the median is .

Based on this information, a new observation can be considered an outlier if it is greater than what?

Possible Answers:

115

100

120

110

Correct answer:

115

Explanation:

Use the $1.5 \cdot IQR$ criteria:

This states that anything less than Q1-1.5IQR or greater than Q3+1.5IQR will be an outlier.

Thus, we want to find

Q3+1.5IQR where IQR =Q3-Q1 .

$1.5 \cdot (70 - 40) =1.5\cdot 30=45$

$Q_3 + (1.5\cdot IQR) = 70 + 45 = 115$

Therefore, any new observation greater than 115 can be considered an outlier.

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Example Question #1 : How To Find Outliers

You are given the following information regarding a particular data set:

Q1:

Q3:

Assume that the numbers 23, 56, 73, 150, 2, 56, 145, and 200 are in the data set. How many of these numbers are outliers?

Possible Answers:

Four

Two

None of the numbers are outliers

Three

One

Correct answer:

Two

Explanation:

In order to find the outliers, we can use the Q1-1.5*IQR and Q3+1.5IQR formulas.

IQR = Q3-Q1 = 86-45 = 41

1.5*IQR = 61.5

Q1-1.5*IQR = 45-61.5 = -16.5

Q3+1.5*IQR = 86+61.5 = 147.5

Only two numbers are outside of the calculated range and therefore are outliers: 150 and 200 .

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Example Question #1 : How To Find Outliers

Use the following five number summary to answer the question below:

Min:

Q1:

Med:

Q3:

Max: 185

Which of the following is true regarding outliers?

Possible Answers:

There is only one outlier in this entire data set.

There are no outliers in this data set.

There are no outliers in the upper side of the data set, but there is at least one outlier on the lower side of the data set.

There is at least one outlier in the lower side of the data set and at least one outlier in the upper side of the data set.

There are no outliers in the lower side of the data set, but there is at least one outlier on the upper side of the data set.

Correct answer:

There is at least one outlier in the lower side of the data set and at least one outlier in the upper side of the data set.

Explanation:

Using the Q1-1.5*IQR and Q3+1.5*IQR formulas, we can determine that both the minimum and maximum values of the data set are outliers.

Q1-1.5*IQR

60-1.5*16=36

Q3+1.5*IQR

76+1.5*16=100

This allows us to determine that there is at least one outlier in the upper side of the data set and at least one outlier in the lower side of the data set. Without any more information, we are not able to determine the exact number of outliers in the entire data set.

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Example Question #1 : How To Find Outliers

87, 75, 79, 87, 88, 85, 89, 90, 75, 79, 105

Which values in the above data set are outliers?

Possible Answers:

105

105, 75, 75

75, 75

90, 105

no outliers

Correct answer:

105

Explanation:

Step 1: Recall the definition of an outlier as any value in a data set that is greater than Q3+1.5*IQR or less than Q1-1.5*IQR .

Step 2: Calculate the IQR, which is the third quartile minus the first quartile, or Q3-Q1 . To find and , first write the data in ascending order.

75, 75, 79, 79, 85, 87, 87, 88, 89, 90, 105 . Then, find the median, which is . Next, Find the median of data below , which is Q1 = 79 . Do the same for the data above to get Q3 = 89 . By finding the medians of the lower and upper halves of the data, you are able to find the value, that is greater than 25% of the data and , the value greater than 75% of the data.

Step 3: Q1-1.5*IQR = 79 - 1.5*10 = 64 . No values less than 64.

Q3+1.5*IQR= 89 + 1.5*10 = 104 . In the data set, 105 > 104, so it is an outlier.

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Example Question #1 : How To Find Outliers

A certain distribution has a 1st quartile of 8 and a 3rd quartile of 16. Which of the following data points would be considered an outlier?

Possible Answers:

Correct answer:

Explanation:

An outlier is any data point that falls $1.5\ast IQR$ above the 3rd quartile and below the first quartile. The inter-quartile range is 16-8=8 and $1.5\ast8=12$ . The lower bound would be 8-12=-4 and the upper bound would be 16+12=28 . The only possible answer outside of this range is .

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AP Statistics : How to find outliers

Study concepts, example questions & explanations for AP Statistics

All AP Statistics Resources

Example Questions

Example Question #1 : How To Find Outliers

Example Question #61 : Data

Example Question #1 : How To Find Outliers

Example Question #1 : How To Find Outliers

Example Question #1 : How To Find Outliers

Example Question #1 : How To Find Outliers

All AP Statistics Resources

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