1. The problem is to solve for the rank correlation coefficient, often called Spearman's rank correlation coefficient, which measures the strength and direction of association between two ranked variables. 2. The formula for Spearman's rank correlation coefficient $r_s$ is: $$r_s = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}$$ where $d_i$ is the difference between the ranks of each pair of observations and $n$ is the number of pairs. 3. Important rules: - Assign ranks to each value in both variables. - Calculate the difference $d_i$ between the ranks of each pair. - Square each difference $d_i^2$. - Sum all squared differences $\sum d_i^2$. - Plug values into the formula to find $r_s$. 4. Intermediate work example: Suppose we have $n=5$ pairs with rank differences $d_i$ as 1, -2, 0, 1, 0. Calculate $d_i^2$: $1^2=1$, $(-2)^2=4$, $0^2=0$, $1^2=1$, $0^2=0$. Sum: $1+4+0+1+0=6$. 5. Substitute into formula: $$r_s = 1 - \frac{6 \times 6}{5(5^2 - 1)} = 1 - \frac{36}{5(24)} = 1 - \frac{36}{120} = 1 - 0.3 = 0.7$$ 6. Interpretation: $r_s=0.7$ indicates a strong positive correlation between the ranks. This method can be applied to any paired ranked data to find the rank correlation coefficient.