Calculate and interpret coefficient

3 Two commentators gave ratings out of 100 for seven sports personalities. The ratings are shown in the table below.

1. Calculate Spearman's rank correlation coefficient for these ratings.
2. State what your answer tells you about the ratings given by the two commentators.

3 An expert tested the quality of the wines produced by a vineyard in 9 particular years. He placed them in the following order, starting with the best. $$\begin{array} { l l l l l l l l l } 1980 & 1983 & 1981 & 1982 & 1984 & 1985 & 1987 & 1986 & 1988 \end{array}$$

1. Calculate Spearman's rank correlation coefficient, \(r _ { s }\), between the year of production and the quality of these wines. The years should be ranked from the earliest (1) to the latest (9).
2. State what this value of \(r _ { s }\) shows in this context.

1. (a) Sketch a scatter diagram of a dataset for which Spearman's rank correlation coefficient is + 1 , but the product moment correlation coefficient is less than 1 .

Two judges were judging cheese at the UK Cheese Festival. There were 8 blue cheeses in a particular category. The rankings are shown below. (b) Calculate Spearman's rank correlation coefficient for this dataset.
(c) By sketching a scatter diagram of the rankings, or otherwise, comment on the extent to which the judges agree.

Two music critics, \(P\) and \(Q\), give scores to seven concerts as follows.

Concert	1	2	3	4	5	6	7
Score by critic \(P\)	12	11	6	13	17	16	14
Score by critic \(Q\)	9	13	8	14	18	16	20

1. Calculate Spearman's rank correlation coefficient, \(r_s\), for these scores. [4]
2. Without carrying out a hypothesis test, state what your answer tells you about the views of the two critics. [1]

Two music critics, \(P\) and \(Q\), give scores to seven concerts as follows.

1. Calculate Spearman's rank correlation coefficient, \(r_s\), for these scores. [4]
2. Without carrying out a hypothesis test, state what your answer tells you about the views of the two critics. [1]