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Standard Deviation of a Ratio X/Y

Calculate the standard deviation of a ratio between two random variables using the delta method

Input Parameters
Results
Enter your parameters and click "Calculate" to see results.
Results for Different Correlation Coefficients
Correlation (ρ) Mean of X/Y SD of X/Y
Methodology Note

This application uses the delta method to approximate the standard deviation of the ratio X/Y. The delta method is a technique for estimating the variance of a function of random variables using Taylor series expansion.

SD(X/Y) ≈ √[(SD_X²/Y²) + (X²·SD_Y²/Y⁴) - (2·X·ρ·SD_X·SD_Y/Y³)]

Where ρ is the correlation coefficient between X and Y. This formula allows us to estimate the standard deviation by considering the means, standard deviations, and correlation between the variables.