Weighted Average: Definition and How It Is Calculated and Used

What Is Weighted Average?

A weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set. A weighted average can be more accurate than a simple average in which all numbers in a data set are assigned an identical weight.

What Is the Purpose of a Weighted Average?

In calculating a simple average, or arithmetic mean, all numbers are treated equally and assigned equal weight. But a weighted average assigns weights that determine in advance the relative importance of each data point. In calculating a weighted average, each number in the data set is multiplied by a predetermined weight before the final calculation is made.

A weighted average is most often computed to equalize the frequency of the values in a data set. For example, a survey may gather enough responses from every age group to be considered statistically valid, but the 18 to 34 age group may have fewer respondents than all others relative to their share of the population. The survey team may weigh the results of the 18 to 34 age group so that their views are represented proportionately.

However, values in a data set may be weighted for other reasons than the frequency of occurrence. For example, if students in a dance class are graded on skill, attendance, and manners, the grade for skill may be given greater weight than the other factors.

Each data point value in a weighted average is multiplied by the assigned weight, which is then summed and divided by the number of data points. The final average number reflects the relative importance of each observation and is thus more descriptive than a simple average. It also has the effect of smoothing out the data and enhancing its accuracy.

Weighting a Stock Portfolio

Investors usually build a position in a stock over a period of several years. That makes it tough to keep track of the cost basis on those shares and their relative changes in value. The investor can calculate a weighted average of the share price paid for the shares. To do so, multiply the number of shares acquired at each price by that price, add those values, then divide the total value by the total number of shares.

For example, say an investor acquires 100 shares of a company in year one at $10, and 50 shares of the same stock in year two at $40. To get a weighted average of the price paid, the investor multiplies 100 shares by $10 for year one and 50 shares by $40 for year two, then adds the results to get a total of $3,000. Then the total amount paid for the shares, $3,000 in this case, is divided by the number of shares acquired over both years, 150, to get the weighted average price paid of $20.

This average is now weighted with respect to the number of shares acquired at each price, not just the absolute price.

Advantages and Disadvantages of Weighted Average

Pros of Weighted Average

Weighted average provides a more accurate representation of data when different values within a dataset hold varying degrees of importance. By assigning weights to each value based on their significance, weighted averages ensure that more weight is given to data points that have a greater impact on the overall result. This allows for a more nuanced analysis and decision-making process.

Next, weighted averages are particularly useful for handling skewed distributions or outliers within a dataset. Instead of being overly influenced by extreme values, weighted averages take into account the relative importance of each data point. This means you can "manipulate" your data set so it's more relevant, especially when you don't want to consider extreme values.

Thirdly, weighted averages offer flexibility in their application across various fields and disciplines. Whether in finance, statistics, engineering, or manufacturing, weighted averages can be customized to suit specific needs and objectives. For instance, like we discussed above, weighted averages are commonly used to calculate portfolio returns where the weights represent the allocation of assets. Weighted averages can also be used in the manufacturing process to determine the right combination of goods to use.

Cons of Weighted Average

One downside of a weighted average is the potential for subjectivity in determining the weights assigned to each data point. Deciding on the appropriate weights can be challenging, and it often involves subjective judgment where you don't actually know the weight to attribute. This subjectivity can introduce bias into the analysis and undermine the reliability of the weighted average.

Weighted averages may be sensitive to changes in the underlying data or weighting scheme. Small variations in the weights or input values can lead to significant fluctuations in the calculated average, making the results less stable and harder to interpret. This sensitivity can be particularly problematic in scenarios where the weights are based on uncertain or volatile factors which may include human emotion (i.e. are you confident you'll feel the same about the appropriate weights over time?).

Last, the interpretation of weighted averages can be more complex compared to simple arithmetic means. Though weighted averages provide a single summary statistic, they may make it tough to understand the full scope of the relationship across data points. Therefore, it's essential to carefully assess how the weights are assigned and the values are clearly communicated to those who interpret the results.

Examples of Weighted Averages

Weighted averages show up in many areas of finance besides the purchase price of shares, including portfolio returns, inventory accounting, and valuation. When a fund that holds multiple securities is up 10% on the year, that 10% represents a weighted average of returns for the fund with respect to the value of each position in the fund.

For inventory accounting, the weighted average value of inventory accounts for fluctuations in commodity prices, for example, while LIFO (last in, first out) or FIFO (first in, first out) methods give more importance to time than value.

When evaluating companies to discern whether their shares are correctly priced, investors use the weighted average cost of capital (WACC) to discount a company’s cash flows. WACC is weighted based on the market value of debt and equity in a company’s capital structure.

Weighted Average vs. Arithmetic vs. Geometric

Weighted averages provide a tailored solution for scenarios where certain data points hold more significance than others. However, there are other forms of calculating averages, some of which were mentioned earlier. The two main alternatives are the arithmetic average and geometric average.

Arithmetic means, or simple averages, are the simplest form of averaging and are widely used for their ease of calculation and interpretation. They assume that all data points are of equal importance and are suitable for symmetrical distributions without significant outliers. Arithmetic means will often be easier to calculate since you divide the sum of the total by the number of instances. However, it is much less nuanced and does not allow for much flexibility.

Another common type of central tendency measure is the geometric mean. The geometric mean offers a specialized solution for scenarios involving exponential growth or decline. By taking the nth root of the product of n values, geometric means give equal weight to the relative percentage changes between values. This makes them particularly useful in finance for calculating compound interest rates or in epidemiology for analyzing disease spread rates.

The Bottom Line

Statistical measures can be a very important way to help you in your investment journey. You can use weighted averages to help determine the average price of shares as well as the returns of your portfolio. It is generally more accurate than a simple average. You can calculate the weighted average by multiplying each number in the data set by its weight, then adding up each of the results together.