Weighted averages take into account the impact of each number on the overall average, making it more accurate than the arithmetic mean. It is necessary when portions are of different values from the total, such as in portfolio management. Calculation involves determining the percentage each number comprises and multiplying it by the corresponding increase in the portfolio.
Calculating a weighted average requires taking into account the impact that each number being averaged has on the overall average. This is an important concept that is used in various financial settings, such as portfolio management or measuring the value of corporate shares. The important thing to remember when calculating a weighted average is that each number included in the average is weighted according to the part of the set it comprises. Checking whether this calculation is correct involves adding up all the numbers involved and then seeing if the weighted averages adequately reflect the impact on the whole.
The reason a weighted average is necessary is because it provides a more accurate representation of a series of numbers than the arithmetic mean. It is possible to use the arithmetic mean if all the amounts averaged are the same percentage of the total. For example, a man who makes two investments of $500 US dollars each and sees a four percent increase and another two percent increase can easily say that his overall investment increased by three percent, or four more. two divided by two.
When it becomes necessary to calculate a weighted average is when the portions are of different values from the total. Again, using the portfolio value example, imagine that a man makes two investments during the course of the year. He invests $200 in a stock that is up 10 percent and invests $800 in another stock that is up 2.5 percent.
Simply taking the arithmetic mean of the two percentage increases, the assumption would be that the portfolio increased 6.25 percent, which is ten times 2.5 percent divided by two. This is inaccurate because the $800 investment occupies a much larger portion of the portfolio than the $200 investment. Calculating a weighted average requires first determining how much of a serving each number comprises. The total portfolio is $1000 USD, or $800 USD added to $200 USD. Once this is determined, it follows that the $800 is 80 percent, or 0.8, of the total, and the $200 is 20 percent, or 0.2.
With these percentages established, the calculation of a weighted average can be completed by multiplying each with the corresponding increase in the portfolio and then adding these totals. Therefore, the 0.8 is multiplied by 2.5, giving an answer of two, and the 0.2 is multiplied by ten, which also gives two. Adding these totals together shows that the portfolio increased by four percent. This can be verified by going back to the original amounts, which shows that the $1,000 portfolio made a profit of $40, an increase of four percent.
Smart Asset.
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