Find out the coefficient of correlation between X and Y series from the data:X 10 12 8 15 20 25 40Y 15 10 6 25 16 12 8

To find the coefficient of correlation between X and Y series, we need to follow these steps:

Step 1: Calculate the mean (average) of X and Y series. Mean of X = (10+12+8+15+20+25+40)/7 = 18.57 Mean of Y = (15+10+6+25+16+12+8)/7 = 13.14

Step 2: Subtract the mean from each data point in X and Y series and square the result. For X: (10-18.57)^2, (12-18.57)^2, (8-18.57)^2, (15-18.57)^2, (20-18.57)^2, (25-18.57)^2, (40-18.57)^2 For Y: (15-13.14)^2, (10-13.14)^2, (6-13.14)^2, (25-13.14)^2, (16-13.14)^2, (12-13.14)^2, (8-13.14)^2

Step 3: Sum up the results from step 2 for both X and Y series.

Step 4: Calculate the product of the differences from the mean for each data point in X and Y series. For example: (10-18.57)(15-13.14), (12-18.57)(10-13.14), (8-18.57)*(6-13.14), etc.

Step 5: Sum up the results from step 4.

Step 6: Divide the sum from step 5 by the square root of the product of the sums from step 3 for X and Y series. This will give you the coefficient of correlation.

Note: The coefficient of correlation ranges from -1 to 1. A value close to 1 indicates a strong positive correlation, a value close to -1 indicates a strong negative correlation, and a value close to 0 indicates no correlation.