What is Weighted Average?
A weighted average is a statistical measurement that considers the varying degrees of importance of numbers in a data set. Unlike a simple average, which treats all values equally, a weighted average assigns different significance to each number, providing a more precise representation of the data.
Key Takeaways
- Relative Importance: A weighted average accounts for the relative importance or frequency of factors in a data set.
- Enhanced Accuracy: Often more accurate than a simple average.
- Calculation: Each data point is multiplied by its assigned weight, summed, and divided by the number of data points.
- Usage: Commonly used by stock investors to track the cost basis of shares bought at varying times.
What Is the Purpose of a Weighted Average?
In calculating a simple average, all numbers are treated equally and assigned equal weight. In contrast, a weighted average assigns weights that pre-determine the relative importance of each data point.
Weighted averages are often computed to equalize the frequency of values within a dataset. For example, a survey may need to represent the 18-34 age group proportionately to get statistically valid results. Similarly, in a dance class, skill may be given more weight compared to attendance or manners.
Each data point value in a weighted average is multiplied by the assigned weight, summarized, and then divided by the total number of data points, providing a more descriptive and accurate measure than a simple average.
| Data Point | Data Point Value | Assigned Weight | Data Point Weighted Value |
|---|---|---|---|
| 1 | 10 | 2 | 20 |
| 2 | 50 | 5 | 250 |
| 3 | 40 | 3 | 120 |
| TOTAL | 100 | 10 | 390 |
| Weighted Average | 39 |
Weighting a Stock Portfolio
Investors frequently buy stock over several years, complicating tracking cost basis and value changes. By calculating a weighted average share price, investors can better manage their portfolio. Multiply the number of shares bought at each price by that price, add those values, and then divide by the total number of shares.
For instance, if an investor buys 100 shares at $10 in year one and 50 shares at $40 in year two, the weighted average price paid is ($10 * 100) + ($40 * 50) / (100 + 50) = $20.
Advantages and Disadvantages of Weighted Average
Pros:
- Accurate Representation: Offers a nuanced analysis by accounting for varying significance levels.
- Handles Outliers: Mitigates the influence of extreme values.
- Flexibility: Applicable across various fields including finance, statistics, and engineering.
Cons:
- Subjectivity: Determining appropriate weights can be challenging and subjective, potentially introducing bias.
- Sensitivity: Weight changes can lead to significant fluctuations, affecting stability.
- Complexity: More complex to interpret compared to simple arithmetic means.
Examples of Weighted Averages
Weighted averages are prevalent in finance for portfolio returns, inventory accounting, and valuation. For example, portfolio returns reflect a weighted average relative to each position’s value. In inventory accounting, weighted averages consider commodity price fluctuations.
Weighted Average vs. Arithmetic vs. Geometric
- Arithmetic Mean: Assumes equal importance for all data points, suitable for symmetrical distributions without significant outliers.
- Geometric Mean: Specially suited for scenarios involving exponential growth or decline, useful in finance to calculate compound interest rates or epidemiology for analyzing disease spread rates.
Frequently Asked Questions
What is Weighted Average?
A weighted average assigns different weights to data points based on their significance, resulting in a more accurate representation of the overall data set.
Is Weighted Average Better?
Weighted averages are better when data points have varying importance. However, they may introduce subjectivity and be sensitive to weight changes.
How Does a Weighted Average Differ From a Simple Average?
A weighted average accounts for the relative contribution or weight of the data points, while a simple average treats all data points equally.
Examples of Weighted Averages in Finance?
Weighted averages in finance include volume-weighted average price (VWAP), the weighted average cost of capital (WACC), and exponential moving averages (EMAs).
How Do You Calculate a Weighted Average?
Compute a weighted average by multiplying each data point’s value by its relative weight, then summing these products and dividing by the total sum of weights.
The Bottom Line
Weighted averages provide a more accurate measure for determining average prices and portfolio returns than simple averages. To calculate a weighted average, multiply each number in the data set by its weight, then add the results together and divide by the sum of the weights.
Related Terms: arithmetic mean, geometric mean, portfolio returns, inventory accounting.
References
- Tax Foundation. “Inventory Valuation in Europe”.
- My Accounting Course. “Weighted Average Cost of Capital (WACC) Guide”.
- CDC. “Measures of Spread”.
