Math Problem Statement

Find the sum of X, Y, XY, X^2, Y^2, and calculate the correlation coefficient r for the given dataset of students' quiz scores in Math (X) and Science (Y).

Solution

Here are the solutions to the given questions based on the data provided:

  1. X=425\sum X = 425
  2. Y=426\sum Y = 426
  3. XY=30221\sum XY = 30221
  4. X2=30755\sum X^2 = 30755
  5. Y2=31504\sum Y^2 = 31504
  6. The value of the correlation coefficient rr is approximately 0.0510.051

Would you like further clarification or a breakdown of any part of the solution?

Here are five related questions:

  1. What does the correlation coefficient rr tell us about the relationship between Math and Science scores?
  2. How is rr affected by the magnitude of XX and YY values?
  3. What are some possible reasons for a low correlation coefficient?
  4. How would you interpret a correlation coefficient close to 1 or -1?
  5. Can rr be influenced by outliers in the data? How?

Tip: The correlation coefficient rr ranges from -1 to 1. The closer it is to these extremes, the stronger the relationship between the variables.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation Coefficient
Summation
Bivariate Data Analysis

Formulas

Sum of X (∑X) = Sum of all X values
Sum of Y (∑Y) = Sum of all Y values
Sum of XY (∑XY) = Sum of products of corresponding X and Y values
Sum of X^2 (∑X^2) = Sum of squares of X values
Sum of Y^2 (∑Y^2) = Sum of squares of Y values
Correlation coefficient (r) = (n(∑XY) - (∑X)(∑Y)) / sqrt((n∑X^2 - (∑X)^2)(n∑Y^2 - (∑Y)^2))

Theorems

Pearson Correlation Coefficient

Suitable Grade Level

High School (Grades 9-12)