Solution:
Given data:

X = 0.854 Y (i.e., X and Y are positively correlated)
Y = 0.89X (i.e., X and Y are positively correlated)
σx = 3

Step 1: Calculation of Coefficient of Correlation (r)
r = √(0.854 * 0.89) = 0.870
Therefore, the coefficient of correlation is 0.870.

Step 2: Calculation of Standard Deviation of Y (σy)
σy = σx / r
σy = 3 / 0.870
σy = 3.448
Therefore, the standard deviation of Y is 3.448.

Explanation:

Coefficient of Correlation (r): It is a measure of the strength and direction of the relationship between two variables. It ranges from -1 to +1. A value of +1 indicates a perfect positive correlation, 0 indicates no correlation, and -1 indicates a perfect negative correlation. In this case, the coefficient of correlation is 0.870, which indicates a strong positive correlation between X and Y.

Standard Deviation of Y (σy): It is a measure of the dispersion or variability of Y values around the mean. In this case, we are given the value of σx, which is the standard deviation of X. We can use the formula σy = σx / r to calculate the standard deviation of Y. Since r is positive, the standard deviation of Y will also be positive. The value of σy is 3.448, which indicates that the Y values are spread out around the mean by an average of 3.448 units.

Conclusion:

In conclusion, the coefficient of correlation between X and Y is 0.870, which indicates a strong positive correlation. The standard deviation of Y is 3.448, which means that the Y values are spread out around the mean by an average of 3.448 units.

From the following data calculate: a coefficient of correlation. b. Standard deviation of y X = 0.854 Y; Y = 0�89 � ; 6x = 3.