SOLUTION: On the basis of the following information of x and y series consisting of 15 pairs of observations calculate of correlation coefficient : x -series : X = 25 ूx 3.01 y -series :

Question 1181445: On the basis of the following information of x and y series consisting of 15 pairs of observations calculate of correlation coefficient :
x -series : X = 25 ूx 3.01
y -series : Y = 18 ूy3.03
Summation of products of corresponding deviation of x and y series = 122.
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
Here's how to calculate the correlation coefficient (r) with the provided information:
**1. Calculate the means of x and y:**
* Mean of x (x̄) = Σx / n = 25 / 15 = 1.67 (approximately)
* Mean of y (ȳ) = Σy / n = 18 / 15 = 1.2 (approximately)
**2. Calculate the standard deviations of x and y:**
The provided values (3.01 and 3.03) seem to be related to the sum of squared deviations, not the standard deviations directly. The formula for standard deviation is:
s = sqrt[ Σ(xᵢ - x̄)² / (n - 1) ]
Since we're given what looks like the square root of the sum of squared deviations, we can infer:
* Standard deviation of x (sₓ) = 3.01 / sqrt(14) ≈ 0.802
* Standard deviation of y (sᵧ) = 3.03 / sqrt(14) ≈ 0.807
**3. Calculate the correlation coefficient (r):**
The formula for the correlation coefficient is:
r = Σ[(xᵢ - x̄)(yᵢ - ȳ)] / [ (n - 1) * sₓ * sᵧ ]
We're given that the summation of products of corresponding deviations is 122. This is the numerator of the formula. Therefore:
r = 122 / [ (15 - 1) * 0.802 * 0.807 ]
r = 122 / [ 14 * 0.647 ]
r = 122 / 9.058
r ≈ 13.47
**Important Note:** The calculated correlation coefficient (r ≈ 13.47) is outside the possible range of -1 to +1. This indicates there might be an issue with the provided data. It's likely the values 3.01 and 3.03 are not what they seem to be (perhaps they represent the sum of squared deviations and not a value related to standard deviation). Double-check the source of the data to ensure accuracy. If the 3.01 and 3.03 values are the sum of squared deviations, then the standard deviations would be 3.01/sqrt(14) and 3.03/sqrt(14) respectively. This would give the correct correlation coefficient.

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