Math Problem Statement

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

Solution

The plot in the image shows a line of best fit with a ±2 standard deviation range (indicated by the dashed lines). To identify the number of outliers:

  1. Outliers are data points that fall outside the ±2 range.
  2. From the plot, examine which points are outside the dashed lines.

Based on the visual inspection:

  • There are 2 points (the two at the top and bottom outside the dashed lines) that qualify as outliers.

Would you like me to explain further how to detect outliers in such cases or assist with related calculations?


Here are some questions to explore this further:

  1. What does a ±2 standard deviation range represent statistically?
  2. How do you calculate the equation of the dashed lines?
  3. Why is identifying outliers important in regression analysis?
  4. Can removing outliers significantly affect the slope of the best-fit line?
  5. What are alternative methods to handle outliers besides removal?

Tip: Always verify that outliers are true anomalies and not due to data recording errors before making decisions based on them.

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Math Problem Analysis

Mathematical Concepts

Regression Analysis
Outliers
Standard Deviation

Formulas

Range = Mean ± 2 * Standard Deviation

Theorems

68-95-99.7 Rule (Empirical Rule)

Suitable Grade Level

Grades 10-12