Math Problem Statement

The following plot shows a line of best fit accompanied by the ±2σ range. How many outliers are present in the data?

Solution

From the provided image, the task is to determine how many outliers are present in the data. Outliers are defined as data points that lie outside the ±2 standard deviation (±2σ) range from the line of best fit (indicated by the dashed lines).

To count the outliers:

  1. Examine all the data points plotted on the graph.
  2. Identify the points that fall outside the dashed boundary lines (±2σ range).
  3. Count these points.

Based on the visual inspection of the graph:

  • There seem to be 2 points that fall outside the dashed lines, which means there are 2 outliers.

If you have further questions or want details clarified, let me know!

Follow-up questions:

  1. What are standard deviations, and how are they used to identify outliers?
  2. How is a line of best fit determined in a regression model?
  3. Why are ±2σ boundaries significant in analyzing data?
  4. What happens if there are too many outliers in a dataset?
  5. Can outliers impact the slope of the line of best fit? Why or why not?

Tip:

Always double-check the dataset's points visually when identifying outliers, as mistakes in interpretation can alter results.

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Math Problem Analysis

Mathematical Concepts

Statistics
Regression Analysis
Outlier Detection

Formulas

Outliers: Data points lying outside ±2 standard deviations from the mean or regression line

Theorems

68-95-99.7 Rule (Empirical Rule)

Suitable Grade Level

Grades 10-12