Calculating a weighted average requires taking into account the impact that each number being averaged out has on the overall average. This is an important concept that is used in various financial scenarios like portfolio management or measuring the worth 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 portion of the whole it entails. Checking to see if this calculation is correct involves totaling up all of the numbers involved and then to see if the weighted averages properly reflect the impact on the whole.
The reason that calculating a weighted average is necessary is that 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 being averaged are the same percentage of the whole. For example, a man who makes two investments of $500 US Dollars (USD) each and sees one rise by four percent and another rise by two percent can easily say that his overall investment rose by three percent, or four plus two divided by two.
When it becomes necessary to calculate a weighted average is when the portions are of different values to the whole. Once again using the example of portfolio worth, imagine that a man makes two investments during course of the year. He invests $200 USD in one stock that goes up by ten percent and invests $800 USD in another stock that goes up 2.5 percent.
Simply taking the arithmetic mean of the two rises in percentage, the assumption would be that the portfolio rose 6.25 percent, which is ten by 2.5 percent divided by two. This is inaccurate because the $800 USD investment takes a much bigger portion of the portfolio than the $200 USD investment. Calculating a weighted average requires first determining how much of a portion 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 USD is 80 percent, or 0.8, of the total, and the $200 USD is 20 percent, or 0.2.
With these percentages in place, calculating a weighted average can be completed by multiplying each with the corresponding rise in the portfolio and then adding these totals together. Thus, 0.8 is multiplied by 2.5, yielding an answer of two, and the 0.2 is multiplied by ten, which also yields two. Adding these totals together shows that the portfolio increased by four percent. This can be checked by going back to the original amounts, which shows that the $1000 USD portfolio gained a profit of $40 USD, a four percent rise.