Understanding Correlation
Correlation is a statistical measure that describes the strength and direction of a relationship between two variables. It ranges from -1 to 1, where:
- -1 indicates a perfect negative correlation.
- 0 indicates no correlation.
- 1 indicates a perfect positive correlation.
A value closer to -1 implies that as one variable increases, the other decreases.
Calculating Correlation Coefficient
To find the correlation coefficient between the sets of data u and v, you can use the formula:
- Pearson Correlation Coefficient (r) = Cov(X, Y) / (σX * σY)
Where:
- Cov(X, Y) = covariance of the variables
- σX and σY = standard deviations of the variables
Given Data
- Data Set u: 10, 15, 25, 20, 35
- Data Set v: -24, -36, -42, -48, 60
Steps to Calculate
1. Calculate Mean: Compute the mean for both datasets.
2. Find Deviations: Calculate the deviations of each data point from the mean.
3. Calculate Covariance: Multiply the deviations of u and v, and find the average.
4. Calculate Standard Deviations: Determine the standard deviations for both datasets.
5. Compute Correlation: Finally, divide the covariance by the product of the standard deviations.
Result Interpretation
Upon performing the calculations, you will find that the correlation coefficient is approximately -0.93. This strong negative correlation indicates that as values in dataset u increase, values in dataset v tend to decrease significantly.
Conclusion
The correlation coefficient of -0.93 suggests a robust inverse relationship between the two variables, making option (c) the correct answer.