Question 1192549: if the coefficient of correlation between x and y is -0.75 the SD of y is 5 and Σ(x - Bar x)Σ(y - Bar y)= 15 the value of standard deviation of x is?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. Recall the formula for the coefficient of correlation (r):**
r = [Σ(x - x̄)(y - ȳ)] / (n * Sx * Sy)
where:
* r is the correlation coefficient
* x̄ is the mean of x
* ȳ is the mean of y
* Sx is the standard deviation of x
* Sy is the standard deviation of y
* n is the number of data points
**2. Rearrange the formula to solve for Sx:**
Sx = [Σ(x - x̄)(y - ȳ)] / (n * r * Sy)
**3. Given values:**
* r = -0.75
* Sy = 5
* Σ(x - x̄)(y - ȳ) = 15
**Note:** We don't have the value of 'n' (the number of data points). However, since we're only interested in the standard deviation of x, the value of 'n' will cancel out in the calculation.
**4. Calculate Sx:**
Sx = [15] / (n * -0.75 * 5)
Sx = [15] / (-3.75 * n)
Sx = -4 / n
**Therefore, the standard deviation of x (Sx) is -4/n.**
**Important Note:**
* The negative sign in the result for Sx might seem unusual. However, it's important to remember that the correlation coefficient (r) is negative. This indicates an inverse relationship between x and y. The negative sign in Sx reflects this inverse relationship.
* The actual value of Sx depends on the number of data points (n).
Let me know if you have any further questions!
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