Math Problem Statement
Construct a scatter diagram for these data.
Calculate the correlation of the coefficient (*r). Interpret the results.
Solution
The scatter plot above shows a negative relationship between the number of absences and final grades, meaning that as the number of absences increases, the final grade tends to decrease.
Correlation Coefficient (r):
The calculated correlation coefficient suggests a strong negative correlation between the two variables. This implies that students with more absences generally have lower final grades. Since is close to -1, it indicates a nearly linear, inverse relationship.
Interpretation:
A strong negative correlation like this often reflects that the variables are highly related, with an increase in absences strongly associated with a drop in grades. While correlation doesn’t imply causation, it strongly suggests that attending class may positively impact students' performance.
Would you like further details on the calculation, or do you have any other questions?
Related Questions:
- How would the correlation change if a student with high absences and high grades were added?
- What would a correlation coefficient close to 0 indicate in this scenario?
- Can the strong correlation suggest causation in real-life contexts?
- How could outliers affect the correlation coefficient?
- What other factors might influence final grades besides absences?
Tip:
A correlation coefficient close to -1 or 1 indicates a strong linear relationship, while values close to 0 indicate a weak or no linear relationship.
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Math Problem Analysis
Mathematical Concepts
Statistics
Scatter Plot
Correlation Coefficient
Formulas
Pearson's Correlation Coefficient Formula: r = Σ((X - X̄)(Y - Ȳ)) / √(Σ(X - X̄)² * Σ(Y - Ȳ)²)
Theorems
Pearson's Correlation Theorem
Suitable Grade Level
Grades 9-12
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