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 rr) 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:

  • xx is the grade of the students
  • yy is the number of pets
  • nn 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