Math Problem Statement
Alfonso surveyed several students in his school. He asked them to give the grade that they are in and the number of pets they have at home. The results are shown in the table below.
Find the correlation coefficient for the data. Round to the nearest hundredth.
Solution
To calculate the correlation coefficient for the data, we need the table that contains the two variables: the grade of the students and the number of pets they have. The correlation coefficient (denoted as ) measures the strength and direction of the linear relationship between two variables, and it can be computed using the formula:
[ r = \frac{n \sum xy - (\sum x)(\sum y)}{\sqrt{\left[n \sum x^2 - (\sum x)^2\right]\left[n \sum y^2 - (\sum y)^2\right]}} ]
Where:
- is the grade of the students
- is the number of pets
- is the number of data points
Please provide the data (the table of student grades and the number of pets) so that I can proceed with the calculation.
Let me know if you'd like help inputting the data!
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Math Problem Analysis
Mathematical Concepts
Statistics
Correlation
Linear Relationships
Formulas
Correlation coefficient formula: r = (nΣxy - ΣxΣy) / √[(nΣx² - (Σx)²)(nΣy² - (Σy)²)]
Theorems
Correlation Coefficient Interpretation
Properties of Linear Correlation
Suitable Grade Level
Grades 9-12
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