Exploring the Geometric Mean of Grouped Data
Keywords:
business, economics, geometric mean, grouped data, unbiased estimate, stock market dataAbstract
We introduce a new method to estimate the geometric mean of grouped data by deriving an unbiased estimate based on uniformly distributed values within class intervals. In the current literature, traditional approaches often rely on class midpoints or geometric means of class endpoints, which may lead to biased results. Our proposed estimator is shown to perform more accurately, particularly when it is applied to financial data, such as the annual growth rates of the S&P 500 index. This study demonstrates the estimator’s effectiveness through both analytical derivation and empirical testing, offering a valuable tool for analysis.
References
Costa, J. (2018, March 23). Calculating Geometric Means (with online calculator). Retrieved from https://buzzardsbay.org/special-topics/calculating-geometric-mean/
Fleming, P.J., & Wallace, J.J. (1986, March). How not to lie with statistics: The correct way to summarize benchmark results. Commun. ACM29, (3), 218–221.
Galton, F. (1879). The geometric mean, in vital and social statistics. Proceedings of the Royal Society of London, 29(196–199), 365–367.
McNichol, D. (2018). On Average, You're Using the Wrong Average: Geometric & Harmonic Means in Data Analysis. Retrieved from https://medium.com/data-science/on-average-youre-using-the-wrong-average-geometric-harmonic-means-in-data-analysis-2a703e21ea0
S&P 500 (^GSPC) Historical Data. (2020). Retrieved from https://finance.yahoo.com/quote/%5EGSPC/history/?frequency=1mo&period1=-1325548800&period2=1577750400
Szatrowski, Z. (1946). Calculating the Geometric Mean from a Large Amount of Data. Journal of the American Statistical Association, 41(234), 218–220.
Watier, N.N., Lamontagne, C., & Chartier, S. (2011). What does the mean mean? Journal of Statistics Education, 19(2).
White, S.R., & Bonnett, L.J. (2019). Biased sampling activity: An investigation to promote discussion. Teaching Statistics, 41(1), 8–13.
