Q.A firm's advertisement expenditure (X, ₹ lakh) and its sales (Y, ₹ lakh) over 5 years are: X: 1, 2, 3, 4, 5 and Y: 2, 4, 5, 4, 5. Calculate Karl Pearson's Coefficient of Correlation between advertisement expenditure and sales.

Correlation measures the degree and direction of relationship between two variables; it is positive when they move together, negative when they move in opposite directions, and ranges from minus 1 (perfect negative) through 0 (no correlation) to plus 1 (perfect positive).

This is a 2-mark short note in the AP Intermediate 2nd-year Economics statistics (correlation analysis) unit.

Correlation refers to the statistical relationship between two variables that tend to change together. It studies whether, and how closely, a change in one variable is associated with a change in another — for example, the relationship between price and demand, or between income and consumption. Correlation is positive (direct) when the two variables move in the same direction (both rise or both fall), and negative (inverse) when they move in opposite directions (one rises as the other falls). The degree of correlation is measured by the coefficient of correlation, whose value lies between minus 1 and plus 1: a value near plu …

Rank correlation measures the closeness of relationship between two variables ranked in order rather than measured exactly, and is especially useful for qualitative data such as beauty, honesty or intelligence. It is computed by Spearman's coefficient, which lies between minus one and plus one. This is an AP Intermediate 2nd-year Economics (statistics) topic.

Meaning: Rank correlation is a method of measuring the degree of association between two variables when their values are given, or can be arranged, in the form of ranks or orders of merit rather than precise numerical measurements. It was developed by the statistician Charles Edward Spearman, and so the measure is called Spearman's rank-correlation coefficient.

Formula: Spearman's rank-correlation coefficient (usually denoted R) is calculated as follows: R equals one minus the quantity six times the sum of the squares of the differences between the ranks of the two variables, divided by n multiplied by (n squared minus one), where the difference for each pair is the rank of the first variable minus the rank of the second, and n is the number of pairs of observations.

Features and uses:

1. Its value lies between minus one and plus one — plus one meaning perfect positive rank agreement, minus one meaning perfect negative (reverse) agreement, and zero meaning no rank correlation.
2. It is especially useful for qualitative data such as beauty, intelligence, honesty or efficiency, which cannot be measured numerically but can be ranked. …