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. 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 can be more accurate than a simple average in which all numbers in a data set are assigned an identical weight.Key Takeaways
- The weighted average takes into account the relative importance or frequency of some factors in a data set.
- A weighted average is sometimes more accurate than a simple average.
- In a weighted average, each data point value is multiplied by the assigned weight, which is then summed and divided by the number of data points.
- A weighted average can improve the data’s accuracy.
- Stock investors use a weighted average to track the cost basis of shares bought at varying times.
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.
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.Weighted Average | |||
---|---|---|---|
Data Point | Data Point Value | Assigned Weight | Data Point Weighted Value |
1 | 10 | 2 | 20 |
1 | 50 | 5 | 250 |
1 | 40 | 3 | 120 |
TOTAL | 100 | 10 | 390 |
Weighted Average | 39 |
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.
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.
How Does a Weighted Average Differ From a Simple Average?
What Are Some Examples of Weighted Averages Used In Finance?
Many weighted averages are found in finance, including the volume-weighted average price (VWAP), the weighted average cost of capital, and exponential moving averages (EMAs) used in charting. Construction of portfolio weights and the LIFO and FIFO inventory methods also make use of weighted averages.