Lesson 14 Outliers

Lesson 14
Outliers

Open Ended

What do you notice? What do you wonder?

What are you thoughts about the value of 10?

We will use the IQR from data sets to help determine if a value is an outlier.

IQR and Outliers

Values in a data set that are greatly different from the rest of the data are called outliers.

What is an outlier?

Outliers

A value will be considered an outlier for a data set if it is greater than Q3 + 1.5 IQR or less than Q1 - 1.5 IQR.

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Determining outliers.

Open Ended

Here is the data set used to create the histogram and box plot from the warm-up. Use technology to find the mean, standard deviation, and five-number summary.

The given values are representing thousands of dollars. So you may put 1.0803 in google sheets as 1,080.30

Find IQR on Google sheets

=SUM(click on value of QUARTILE 1 - click on value of QUARTILE 3)

Find 1.5 of IQR

=PRODUCT(click on value of IQR, 1.5)



If you are using google sheets you should get an answer of 3.9752625.

Is the maximum value of 9.8923 an outlier?

• Figure out if the maximum value is an outlier

• Is the maximum greater than Q3+1.5(IQR)?

• Q3 is approximately 4.8 and 1.5(IQR) is approximately 3.9

• So...... is 9.8923 an outlier?

Multiple Choice

• Figure out if the maximum value is an outlier

• Is the maximum greater than Q3+1.5(IQR)?

• Q3 is approximately 4.8 and 1.5(IQR) is approximately 3.9

• So...... is 9.8923 an outlier?

• yes

• no

The next slide will present you with the number summaries.
It may be helpful to write the summaries down to answer questions.

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Let's think about the source of outliers and whether or not we should include them when analyzing data.

The number of property crime (such as theft) reports is collected for 50 colleges in California. Some summary statistics are given:

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Open Ended

Are ANY of the values outliers? Explain your reasoning.

Any means high values or low.

Open Ended

If there are any outliers, why do you think they might exist? Should they be included in an analysis of the data?

Remember, this data set represents the number of property crime (such as theft) reports is collected for 50 colleges in California

The next two questions described here each have an outlier. For each situation, how would you determine if it is appropriate to keep or remove the outlier when analyzing the data?

Open Ended

A number cube has sides labeled 1–6. After rolling 15 times, Tyler records his data:
1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 20

Should you eliminate 20?

​YES!

The outlier, 20, should be eliminated because it is not a plausible value. That is, a number cube cannot roll the number 20.

Open Ended

The dot plot represents the distribution of the number of siblings reported by a group of 20 people.

Should you eliminate 12?

????

The outlier, 12 siblings, should be investigated further to see if it was a data collection error before it is removed. While it is unusual for someone to have 12 siblings, it is still possible.
If it is not an error or if it cannot be determined, it should be kept for any further analysis.

Why is it important to analyze the source of outliers?

To determine if there is a reason to exclude the data from an analysis.

What are reasons to keep an outlier in a data set?

Just because a value is extremely large or small does not discount its reality.
To be honest in the analysis, all valid data should be included.

What are reasons to remove an outlier from a data set?

If there is an error in data collection or recording, the data may be faulty and it would not be honest to include data that does not fit the question asked.

What could be done about the 3 outliers for the college crime data to account for school size as the source of the outliers?

Let's get more specific about the question being asked to collect the data.
The question could be changed to examine crime at schools with enrollment below some level. It may make better sense to look at “crime rate” like a measure of crimes per 100 students or something similar that takes into account the school size rather than just the number of crimes.

How do you know that a value is an outlier?

If it is greater than the third quartile by more than one and a half times the interquartile range or less than the first quartile by the same amount.

Open Ended

A group of 20 students are asked to report the number of pets they keep in their house. The results are
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 21

Open Ended

1. After being told that they should not count any fish in the report, the value of 3 becomes a 2 and the value of 21 becomes 1. Would these changes affect the median, mean, standard deviation, or interquartile range? If so, would each measure decrease or increase from their original values?