*The Business Professor*, updated July 29, 2019, last accessed December 4, 2020, https://thebusinessprofessor.com/lesson/weighted-average-definition/.

### Weighted Average Definition

In arithmetic or mathematical calculation, a weighted average refers to average results realized when each datum is multiplied by an established weight. The multiplication is done before the average of the data set is calculated. Although the weight is predetermined, all the components of the data have an equivalent proportion and thereby carry the same portion of the weight.

The major key takeaways of a weighted average are:

- A weighted average is more detailed than a simple average.
- The relative importance of components of a data set are taken into consideration when calculating a weighted average.
- A weighted average is a mathematical calculation used in inventory accounting and estimation.

### A Little More on What is Weighted Averages

A weighted average contains more details than a simple average, it reflects beyond the average number of a data set. There are many components or observations that make up a data set, when calculating the weighted average of the data set, all observations are regarded as equal and thereby assigned equal weights, before the weighted average is realized, all the components must be multiplied by an established weight. It is important to know that the importance allocated to component in a date set can vary due to certain conditions. Generally, weighted average is important inÂ identifying the importance of each component of a data set.

### Calculation of a Weighted Average of a Stock Portfolio

A weighted average is also useful in calculating the cost basis of a stock portfolio. There are some market factors and trends that affect the performance of a stock portfolio such as changes in stock price. To calculate the weighted average of a stock portfolio, the shares in the portfolio are multiplied by the price paid for each share. Once this is done, the values realized are added and the overall value is divided by the overall number of shares in the stock portfolio. The number of shares in the portfolio and the number of shares bought at a particular price are important when calculating the weighted average.

### Examples of Weighted Averages

There are many instances where a weighted average as a mathematical calculation can be used. A weighted average is calculated, not only for stock portfolio but also for inventory accounting and valuation. When used for inventory accounting and calculation, the weighted average places importance on the value of inventory and prices of goods.

### References for** â€ś**Weighted Averageâ€ť

- https://www.investopedia.com â€ş … â€ş Financial Statements
- https://en.wikipedia.org/wiki/Weighted_arithmetic_mean
- financeformulas.net/Weighted_Average.html

### Academic research for â€śWeighted Averageâ€ť

The weighted average cost of capital, perfect capital markets, and project life: a clarification, Miles, J. A., & Ezzell, J. R. (1980). *Journal of financial and quantitative analysis*, *15*(3), 719-730.

Weighted average finite difference methods for fractional diffusion equations, Yuste, S. B. (2006). *Journal of Computational Physics*, *216*(1), 264-274.

Weighted average importance sampling and defensive mixture distributions, Hesterberg, T. (1995). *Technometrics*, *37*(2), 185-194.

The Kaplanâ€“Meier estimator as an inverse-probability-of-censoring weighted average, Satten, G. A., & Datta, S. (2001). *The American Statistician*, *55*(3), 207-210.

Efficiency of weighted average derivative estimators and index models, Newey, W. K., & Stoker, T. M. (1993). *Econometrica: Journal of the Econometric Society*, 1199-1223.

A weighted average of sparse representations is better than the sparsest one alone, Elad, M., & Yavneh, I. (2009). In *Dagstuhl Seminar Proceedings*. Schloss Dagstuhl-Leibniz-Zentrum fĂĽr Informatik.

Weighted average consensus-based unscented Kalman filtering, Li, W., Wei, G., Han, F., & Liu, Y. (2015). *IEEE transactions on cybernetics*, *46*(2), 558-567.

A unified model between the weighted average and the induced OWA operator, Merigo, J. M. (2011). *Expert Systems with Applications*, *38*(9), 11560-11572.

Non-uniform weighted average sampling and reconstruction in shift-invariant and wavelet spaces, Aldroubi, A. (2002). *Applied and Computational Harmonic Analysis*, *13*(2), 151-161.

The weighted average cost of capital as a cutoff rate: A critical analysis of the classical textbook weighted average, Arditti, F. D., & Levy, H. (1977). *Financial Management*, 24-34.