Learning Target: I can find and interpret clusters, gaps, and outliers on a data display.

Cluster 

A cluster is a group of things that are bunched together.  In statistics, a cluster in formed when several data points lie in a small interval.

Gap 

A gap is a space.  In statistics, it is an interval or section that contains no data.

Outlier

An outlier is a data point that has a value much greater or much less that the other data in the set.  It is set off by itself, atypical, or unusual.

Line Plot

A diagram that uses a number line to display data.

Example 1

The line plot below shows the masses in whole kilograms of salmon caught by fishermen along the Columbia River in the Pacific Northwest.

Use the line plot to describe the data set.

The mean for this data is 121 ÷ 20 or about 6 kilograms.

The median is 5.5 kilograms.

The mode is 5 kilograms.

The range is 11 kilograms.

Example 2

How are the mean, the median, the mode, and the range affected if the outlier, 14 kilograms, is excluded from the data set?  Which statistic changes the most?

Find the mean, median, mode, and range without the outlier.

The median changes from 5.5 kg to 5 kg. 

The mode is unchanged. 

The range changes from 11 kg to 6 kg.

Without the outlier, the mean and median decrease, while the mode stays the same.  The range decreases by 5 kilograms. 

The range changes the most.

Let's Practice Together

55, 62, 66, 71, 72, 72, 74, 108

2.  Suppose the outlier is not in the data set. 

Which measure of center best represented the data set without the outlier?

Which measurement (mean, median, mode, or range) changes most without the outlier?

Your Turn

Last summer, Javier worked for 14 weeks at a music store.  Use the hours he worked below for Exercises 3 and 4.

5, 6, 21, 22, 23, 23, 24, 25, 25, 26, 26, 26, 27, 29

3.  Make a line plot of the data.  Identify and clusters, gaps, and outliers.  Find the mean, median, and mode.

4.  Suppose the outliers were excluded from the data set.  Compare the mean, median, and mode with and without the outliers.

Check for Understanding

A group of students in Mrs. Carter's class took a quiz, and their scores are as follows:

72, 97, 82, 92, 68, 80, 51, 75, 100, 85, 100, 90, 72, 95, 92

1.  What is the mean score?

2.  What would the mean score be (to the nearest tenth) if the outlier were removed?

Answers

1.  mean = 72.5;  median = 71.5;  mode = 72;  range = 53

2.  mode; range

3. 


mean = 22;  median = 24.5;  mode = 26

4.  mean = 24.75;  median = 25;  mode = 26
The mean and median increased; the mode did not change.

Check for Understanding

1.  83.4

2.  85.7