L2 Outliers and Trimmed Mean
Completion requirements
Unit E: Statistics and Probability
Chapter 1: Statistics
Outliers and Trimmed Mean
John and Cynthia are servers at a local café. They compare the tips they received with the total amount of each bill. The tips are recorded in a table.
| Bill Total ($)
|
Tip ($)
|
|---|---|
| 9.00
|
1.25 |
| 8.00
|
1.50 |
| 20.00
|
0.00 |
| 15.00
|
2.25 |
| 23.00
|
10.00 |
| 17.00
|
3.75 |
| 25.00
|
3.50 |
| 22.00
|
3.00 |
| 30.00
|
5.00 |
The data is plotted to compare the tips received with the bill total. The line of best fit is then drawn.
When Cynthia reviewed the graph, she realized that the outliers, (20.00, 0.00) and (23.00, 10.00), do not provide a good representation of the data. The outliers dramatically changed the slope of the line of best fit.
When Cynthia reviewed the graph, she realized that the outliers, (20.00, 0.00) and (23.00, 10.00), do not provide a good representation of the data. The outliers dramatically changed the slope of the line of best fit.
The line of best fit that is influenced by outliers does not represent the data set fairly.
Based on their previous knowledge of scatterplots, they recalled that outliers distort or skew the line of best fit.
Therefore, outliers should not be considered when drawing the line of best fit.
Therefore, outliers should not be considered when drawing the line of best fit.
The line of best fit more accurately represents the data set when it is drawn after excluding any outliers.
Outliers can also dramatically influence the results when calculating measures of central tendency. How should outliers be treated when determining the mean in statistics?
By the end of this lesson, you will be able to
- identify the outlier(s) in a set of data
- explain the effect of outliers on mean, median, and mode
- calculate the trimmed mean for a set of data and justify the removal of outliers
- explain how measures of central tendency and outliers are used to provide various interpretations of data
- solve real-life problems that involve measures of central tendency