Math Problem Statement

Which could likely be the variables represented in the scatter plot shown? Options include: A. The population of a city and the number of houses in the city. B. The population of a city and the number of letters in the city's name. C. The number of cars in a city and the pollution level of the city. D. The number of buildings in a city and the number of trees in the city.

Solution

The scatterplot shown in the question depicts a negative correlation, where one variable decreases as the other increases. Let’s analyze the options to find the most plausible answer:

  1. Option A: The population of a city and the number of houses in the city.
    This likely has a positive correlation, as more population typically results in more houses.

  2. Option B: The population of a city and the number of letters in the city’s name.
    There is no reasonable relationship between population and the number of letters in a city's name.

  3. Option C: The number of cars in a city and the pollution level of the city.
    This could show a positive correlation because more cars typically result in higher pollution, not the negative trend observed.

  4. Option D: The number of buildings in a city and the number of trees in the city.
    This is the best match, as a negative correlation could exist—more buildings may lead to fewer trees due to urban development.

Correct Answer: D.

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Related Questions:

  1. How do positive and negative correlations differ in scatterplots?
  2. What are real-world examples of variables that exhibit negative correlation?
  3. What factors influence correlations between urban development and environmental features?
  4. How can scatterplots be used to predict future trends in data?
  5. Why might some variables have no correlation?

Tip: When interpreting scatterplots, always evaluate whether the relationship between the two variables makes logical sense.

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Math Problem Analysis

Mathematical Concepts

Scatterplots
Correlation Analysis
Negative Correlation

Formulas

No specific formula used

Theorems

Correlation and Causation

Suitable Grade Level

Grades 8-10