Math Problem Statement

The prices and total floor areas of a sample of houses for sale are shown in the scatterplot. Identify the type of correlation from the scatterplot and interpret the correlation in the context of the problem.

Solution

To solve the problem, we need to analyze the scatterplot provided and identify the type of correlation between the variables. The scatterplot shows the relationship between the price of houses (in thousands of dollars) and their total floor area (in square feet).

Analysis:

  1. Type of Correlation: Looking at the scatterplot, we observe that as the total floor area of the houses increases, the price also tends to increase. The data points roughly follow an upward trend. Therefore, the correlation is positive.

  2. Interpretation in Context: The positive correlation in the scatterplot indicates that there is a relationship between the size of a house (measured in square feet) and its price. Specifically, larger houses (with more square footage) tend to have higher prices. This makes sense in a real-world context, as generally, the price of a house increases with its size due to the increased space and potentially more features or amenities.

Would you like more details or have any other questions about this? Here are some additional questions to consider:

  1. What does a negative correlation look like on a scatterplot?
  2. How can we determine the strength of a correlation from a scatterplot?
  3. What is the meaning of a "no correlation" scenario in a scatterplot?
  4. How can outliers affect the interpretation of data in scatterplots?
  5. What are some real-world examples where a positive correlation is observed?

Tip: When interpreting scatterplots, always look for the overall pattern (trend) and check for any deviations or outliers that might affect the correlation.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Scatterplots

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10