Correlation coefficient is a pure number

The correct answer is option 'A', True. The correlation coefficient is indeed a pure number. Let's delve into the details to understand why this is the case.

Understanding Correlation Coefficient

The correlation coefficient is a statistical measure that determines the strength and direction of the relationship between two variables. It quantifies the degree to which the variables are associated with each other. The correlation coefficient ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

Interpretation of Correlation Coefficient

The correlation coefficient provides valuable information about the relationship between variables. Here's how to interpret different values of the correlation coefficient:

- If the correlation coefficient is close to +1, it indicates a strong positive correlation. This means that as one variable increases, the other variable also tends to increase.

- If the correlation coefficient is close to -1, it indicates a strong negative correlation. This means that as one variable increases, the other variable tends to decrease.

- If the correlation coefficient is close to 0, it indicates little to no correlation. This means that there is no consistent relationship between the variables.

Properties of Correlation Coefficient

The correlation coefficient possesses certain properties that make it a pure number:

1. Independence of Units: The correlation coefficient is independent of the units in which the variables are measured. It only measures the strength and direction of the relationship, regardless of the scale or units of the variables.

2. Symmetry: The correlation coefficient is symmetric, meaning that the correlation between variable A and variable B is the same as the correlation between variable B and variable A. It does not matter which variable is considered the dependent or independent variable.

3. Range: The correlation coefficient is bounded between -1 and +1. This range ensures that the coefficient remains a pure number, representing the strength of the relationship without any additional scaling or transformation.

Conclusion

In conclusion, the correlation coefficient is a pure number that quantifies the strength and direction of the relationship between two variables. It is independent of the units of measurement, symmetric, and bounded between -1 and +1. Therefore, the correct answer is option 'A', True.