Explain the difference between Karl Pearson’s correlation co-efficient and spearsman’s rank correlations co-efficient. Under what situations, in the latter preferred to the former?

Karl Pearson's correlation coefficient and Spearman's rank correlation coefficient are two different measures used to quantify the strength and direction of the relationship between two variables. While Pearson's correlation coefficient is suitable for linear relationships between two continuous variables, Spearman's rank correlation coefficient is more appropriate when dealing with ordinal or ranked data, or when the relationship between variables is not linear.

Karl Pearson's Correlation Coefficient:
Pearson's correlation coefficient, denoted by r, measures the linear relationship between two continuous variables. It takes values between -1 and 1, where:

- r = 1 indicates a perfect positive linear relationship
- r = -1 indicates a perfect negative linear relationship
- r = 0 indicates no linear relationship

The formula for Pearson's correlation coefficient is:

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