Weighted Average: What Is It?
A weighted average is a computation that considers the different significance levels of a data set’s numbers. Every integer in the data set is multiplied by a predefined weight before the weighted average is calculated. When all the values in a data collection are given the same weight, a simple average may not be as accurate as a weighted average.
What does a weighted average serve as?
When determining the arithmetic mean or simple average, each integer is given the same weight and treatment. However, a weighted average allocates weights that ascertain each data point’s relative value beforehand.
A weighted average is often calculated to balance out the frequency of the values in a data collection. For instance, a survey may have enough replies from each age group to be deemed statistically valid, but compared to all other age groups, the 18–34 age group may have the fewest respondents. To fairly reflect the opinions of this age range, the survey team may weigh the findings of this age group.
However, data collection values may be weighted for purposes other than frequency of occurrence. For instance, in a dancing class where students are rated on skill, attendance, and etiquette, the skill grade can be weighted more than the other two.
A weighted average multiplies each data point’s value by the specified weight, adds them all together, and divides the result by the total number of data points. Compared to a simple average, the final average number is more descriptive since it represents the relative value of each observation. Additionally, it improves the accuracy of the data by smoothing it out.
How to Balance a Stock Portfolio
Investors often accumulate a stock holding over several years, making monitoring the cost basis of such shares and their respective value fluctuations difficult. To do this, the investor may compute a weighted average of the share price paid for the shares. To do this, divide the entire value by the total number of shares, add the values, and then multiply the number of shares purchased at each price by that price.
Arriving at a weighted average involves assessing each data point’s relative value beforehand.
For example, an investor buys 50 shares of the same stock in year two for $40 and 100 shares of the firm in year one for $10. The investor multiplies 100 shares by $10 for the first year and 50 claims by $40 for the second year to get a weighted average of the price paid. The total comes to $3,000. Next, divide the total cost of the shares—in this case, $3,000—by the total number of shares purchased over both years, which comes to $20.
Rather than only considering the absolute price, this average is weighted based on the quantity of shares purchased at each price.
The weighted mean is another name for the weighted average.
Weighted Average Examples
In addition to the share purchase price, weighted averages are used in inventory accounting, valuation, and portfolio returns. A fund that invests in various assets and is up 10% annually shows a weighted average of returns based on the value of each position in the fund.
In inventory accounting, the weighted average value of inventory, for instance, considers commodity price variations. At the same time, the LIFO (last in, first out) or FIFO (first in, first out) techniques prioritize time over value.
The weighted average cost of capital (WACC) is a tool investors use to discount a company’s cash flows and assess whether its shares are reasonably valued. WACC is weighted based on the market value of the debt and equity in a company’s capital structure.
What distinguishes a simple average from a weighted average?
A basic average does not consider the relative weight or contribution of the items being averaged; a weighted average does. As a result, it assigns more weight to average things that appear more often.
Which Weighted Averages Are Used in Finance, and What Are Some Examples?
The volume-weighted average price (VWAP), the weighted average cost of capital, and the exponential moving averages (EMAs) used in charting are just a few examples of the many weighted averages utilized in finance. Weighted averages are also used in the LIFO and FIFO inventory systems and the construction of portfolio weights.
How is a weighted average calculated?
You may get a weighted average by multiplying the relative proportion or percentage by each number and summing the resulting sums. A portfolio with a weighted average return of 55% equities, 40% bonds, and 5% cash would multiply its weights by the portfolio’s performance each year. In other words, the weighted average return would be (55 × 10%) + (40 × 5%) + (5 × 2%) = 7.6% if the returns on stocks, bonds, and cash were 10%, 5%, and 2%, respectively.
The Final Word
Statistical metrics have the potential to be a handy tool for you while you invest. Weighted averages are valuable for calculating portfolio returns and share average prices. Compared to a simple average, it is often more accurate. You can get the weighted average by multiplying each value in the data set by its weight and adding up all the results.
Conclusion
- The weighted average considers how often or essential certain aspects are in data collection.
- Sometimes, a weighted average yields better results than a simple average.
- Each data point value is multiplied by the given weight in a weighted average, then added together and divided by the total number of data points.
- A weighted average may improve the accuracy of the data.
- Stock investors use a weighted average to monitor the cost basis of shares acquired at diverse dates.
