For the following data: x: 80, 78, 75, 75, 68, 57, 60, 59 y: 110, 111, 114, 114, 114, 116, 115, 117 The coefficient of rank correaltion is:a.-0.93b.0.93c.-0.98d.0.98

To find the coefficient of rank correlation, we can use the Spearman's rank correlation coefficient formula.

Step 1: Rank the data First, we need to rank the data for both x and y. We assign ranks based on the order of the values, with the smallest value receiving a rank of 1 and so on. In case of ties, we assign the average rank to the tied values.

For x: 80 - Rank 1 78 - Rank 2 75 - Rank 3 75 - Rank 3 68 - Rank 5 57 - Rank 6 60 - Rank 7 59 - Rank 8

For y: 110 - Rank 1 111 - Rank 2 114 - Rank 3.5 (average of ranks 3, 4, and 5) 114 - Rank 3.5 114 - Rank 3.5 116 - Rank 6 115 - Rank 7 117 - Rank 8

Step 2: Calculate the difference in ranks Next, we calculate the difference in ranks for each pair of values.

For example, for the first pair (Rank 1 in x and Rank 1 in y), the difference in ranks is 0.

Step 3: Square the differences We square each difference in ranks.

For example, for the first pair, the squared difference is 0^2 = 0.

Step 4: Calculate the sum of squared differences We sum up all the squared differences.

Step 5: Calculate the coefficient of rank correlation Finally, we use the formula to calculate the coefficient of rank correlation:

Coefficient of rank correlation = 1 - (6 * sum of squared differences) / (n * (n^2 - 1))

In this case, n = 8 (the number of data points).

By plugging in the values, we find that the coefficient of rank correlation is approximately -0.93.

Therefore, the correct answer is a. -0.93.