Which of the following provides a numerical measure of correlation between two…

Concept

A correlation coefficient is a numerical summary of the direction and strength of association between two variables. For ordinal or ranked observations, Spearman’s rank-correlation coefficient is computed from the ranks rather than raw measurement units.

Application

The question asks for a numerical measure for two ranked variables. The coefficient of rank correlation returns a value from −1 to +1, so it directly quantifies their monotonic association.

Contrast

• A scatter diagram plots paired observations and gives a visual impression of their joint pattern; it is not itself a numerical rank-based coefficient.

• A frequency distribution groups observations by value or class and records their counts; it does not preserve paired ranks across two variables.

• A two-way table records joint frequencies for categories of two variables; a separate association statistic is needed to quantify the relationship.

• A rank-correlation coefficient uses paired ranks to express both direction and strength in a single dimensionless number.

Cross-check

As paired ranks become more similar, the coefficient approaches +1; when their orders are reversed, it approaches −1. Therefore, the required numerical method is the coefficient of rank correlation.