Math Problem Statement

Which statement is TRUE regarding the added point? a) It is an outlier in the x-direction. b) It is an outlier in the y-direction.

Solution

In the scatter plot shown in the image, the data points represent a relationship between "Weight (in hundreds of pounds)" and "Miles per Gallon (mpg)." The black points follow a general pattern, showing that as the weight of the vehicle increases, its fuel efficiency (miles per gallon) decreases.

There is also a light blue point that has been added, and the question asks whether this added point is an outlier in the x-direction or the y-direction.

  • X-direction: This refers to the horizontal axis (weight in hundreds of pounds). If a point is far from the other points in the horizontal direction, it's an x-direction outlier.
  • Y-direction: This refers to the vertical axis (miles per gallon). If a point is far from the other points in the vertical direction, it's a y-direction outlier.

Observations:

  • The added light blue point has a much lower weight than the other data points, which are clustered between 10 to 40 (hundreds of pounds). The added point is around 5 on the x-axis.
  • The added point has a similar miles per gallon (around 20 mpg) compared to the black points, meaning it aligns in the vertical direction.

Conclusion:

The added point is much further from the rest of the data in the x-direction, meaning it is an x-direction outlier.

Therefore, the correct answer is:

  • a.) It is an outlier in the x-direction.

Would you like further clarification or details on this? Here are five related questions to explore the topic more:

  1. What is the definition of an outlier in statistics?
  2. How does an outlier affect the correlation between two variables?
  3. What techniques can be used to identify outliers in a dataset?
  4. Can an outlier affect the slope of a regression line, and how?
  5. What are potential reasons for data points to appear as outliers in real-world datasets?

Tip: Always consider both the x and y directions when analyzing scatter plot outliers, as a point can be an outlier in either or both directions!

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Math Problem Analysis

Mathematical Concepts

Statistics
Scatter Plot
Outliers

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12