Definition
An average, in finance, is the result obtained by adding together several amounts and then dividing this total by the number of amounts. On the other hand, a weighted average gives different weights or levels of importance to different amounts before calculating their average. This means that each number contributes differently to the final average in a weighted average, rather than being equally considered as in a simple average.
Key Takeaways
- An average is a single value that represents the central point or typical value in a data set derived by dividing the sum of the values with the number of values while a weighted average assigns a weight to each value based on its significance or frequency, and then averages the sum of these products.
- In contexts where all variables contribute equally, the average (or arithmetic mean) is suitable. However, when certain values have more significance or relevance compared to others, a weighted average provides a more accurate overview of the data set.
- The weighted average is more nuanced as it takes into consideration the importance of different data points. However, it is also more complex to calculate compared to the simple average.
Importance
Understanding the difference between an average (simple average) and a weighted average is crucial in finance as they provide different kinds of information and can greatly affect financial analysis and decision-making.
A simple average evenly allocates importance or weight to each value in the set, making it a useful tool for understanding an overall trend or general performance.
However, a weighted average assigns different weights or importance to different values in the set, which is very important in financial contexts where some values have more influence or significance than others.
Examples include portfolio performance evaluation, where different investments have different proportions, or cost of capital calculations, where various sources of capital contribute different amounts.
Thus, the use of averages vs weighted averages can impact the outcome and interpretation of financial analyses, which subsequently affect decision making.
Explanation
The terms ‘Average’ and ‘Weighted Average’ are commonly used in finance, particularly in areas such as portfolio management, stock market analysis, and corporate finance. The key purpose of ‘Average’ (often referred to as mean) is to determine the central tendency or typical value in a data set by calculating the sum of the values divided by number of values. On the other hand, ‘Weighted Average’ is utilized when some values in a data set are of more significance or carry more ‘weight’ than others.
It considers the relative importance of particular values and evaluates a more accurate average by giving different weights to each data point. The importance of these concepts is broad reaching. A simple average might be useful in determining, for instance, the average share price of a company over a period, which can provide a simplified view on its performance.
However in complex scenarios, such as calculating the average return on a stock portfolio, where different stocks hold different proportions, a weighted average is more appropriate. It provides a more realistic evaluation as it considers the relative weightage or proportion of each investment in the portfolio. The method of using weighted average ensures the higher relevance or significance is attributed to the values that have a greater impact on the final result.
Examples of Average vs Weighted Average
**Investment Portfolio**: Let’s say an investor has a portfolio with three investments. Investment A provides an annual return of 6%, Investment B gives 8%, and Investment C yields 10%. The simple or ‘average’ return is (6% + 8% + 10%) / 3 = 8%. But if the total amount invested in A, B, and C is not equal, then this average return doesn’t accurately reflect the portfolio’s performance. If 50% of the investment is in A, 30% in B, and 20% in C, then using the Weighted Average will provide a more accurate representation of the portfolio’s return: (50 * 6%) + (30 * 8%) + (
20 * 10%) =4%.**Grading System**: Consider a class where students’ final grades are based on assignments, mid-term tests, and a final exam. Let each of these components have a different weight: assignments 30%, mid-term test 30%, and final exam 40%. The average score would treat all components equally, which doesn’t reflect the actual grading policy. If a student scored 70 in assignments, 80 in mid-terms, and 90 in the final exam, the weighted average score would be (70*
30)+(80*30)+(90*40)=
**Product Rating**: An online e-commerce platform sells a product, and it has been reviewed by 200 customers. Out of these, 50 gave it a rating of 1 star, 100 gave it 3 stars, and 50 gave it 5 stars. The average (arithmetic mean) rating would be (1+3+5)/3 = 3 stars. However, this doesn’t accurately represent customer opinion as it doesn’t take into account that the number of people who rated each category varies. Using a weighted average takes into consideration the number of people in each category: (50*1 + 100*3 + 50*5) / 200 = 3 stars. Even though the results are the same in this example, this isn’t always the case and weighted average often provides a more accurate representation.
FAQ Section: Average vs Weighted Average
What is an average?
An average is a statistical mean that represents the sum of a set of numbers divided by the count of numbers in the dataset. It gives a central value or the middle value for data.
What is a weighted average?
A weighted average differs from a simple average in that instead of each data point contributing equally to the overall average, some data points contribute more than others. In other words, each number in the dataset has a weight or importance related to it. The sum of the product of each number and its corresponding weight is then divided by the sum of the weights to get the weighted average.
When would you use a simple average vs a weighted average?
A simple average is used when each number in the dataset has an equal significance or weight. On the other hand, you use a weighted average when different numbers carry different levels of importance. For instance, a weighted average would be used to calculate your GPA, as your grades in higher credit classes contribute more than those in lower credit classes.
Can you give an example of a weighted average?
Suppose we have two exams: one is worth 40% of the grade and another is worth 60%. If you score 70 on the first exam and 80 on the second, your weighted average grade would be: (70*40% + 80*60%) = 76.
What is the formula for calculating a weighted average?
The formula for calculating a weighted average is:
Sum of (Value * Weight) / Sum of Weights
Related Entrepreneurship Terms
- Statistical Average: In finance, it is the mean figure calculated by adding the data points in a series and then dividing the total sum by the number of data points.
- Weight: It pertains to the relative importance or influence of a data point in a series. In terms of finance, each data point, such as investment, may carry a different ‘weight’ based on its size or amount.
- Weighted Average Cost of Capital (WACC): It’s the rate a company is expected to pay on average to finance its assets. It’s calculated by taking the average of the required returns, weighted by their respective proportions in the firm’s capital structure.
- Portfolio Weight: This refers to the percentage each holding comprises in an investment portfolio. In a weighted average finance context, the weight of each investment affects the overall returns.
- Weighted Average Maturity (WAM): In finance, it’s the average time until a portfolio’s securities mature, weighted in proportion to the dollar amount invested in the portfolio.
Sources for More Information
- Investopedia: This is a comprehensive resource dedicated to investing and personal finance; it includes definitions, articles, and calculators to help understand finance terms like Average and Weighted Average.
- Corporate Finance Institute: This institute provides online training and certification programs to help users understand complex financial terms and models.
- Khan Academy: A non-profit e-learning platform providing in-depth lessons in many subjects, including finance and capital markets.
- Coursera: It hosts online courses from top universities around the world, and there are many on finance that may delve into topics such as Average versus Weighted Average.
