Understanding the weighted average
A weighted average is an average that takes into account the importance of each number you average. When you find the average (or mean) of a set of numbers, usually all you have to do is add up the numbers and then divide the sum by the number of values you have added. The weighted average assigns importance (or weight) to each number.
Averages are standard statistical tools that can be used to find an approximate midpoint in a set of numbers. The problem with finding the average of a set of numbers is that it does not take into account the relative importance of those numbers.
Weighted averages remedy this deficiency by assigning importance to each number and taking this importance into account when calculating the average. Weighted averages are valuable because they provide more information than a simple average, without requiring much additional information – only the information needed to assign weights to each number.
What is the weighted average method?
The weighted average method is a method of determining the average cost of a product or investment. Companies often use this method to track the value of inventory. Investors can use it to track the cost basis for investments where first-in-first-out (FIFO) or last-in-first-out (LIFO) cost bases are not used.
The advantage of using the weighted average method is that it is easier to track. Systems such as FIFO or LIFO require individual tracking of each unit. This means that businesses must track each unit of each item in the inventory and investors must track the underlying value of each stock they own.
The disadvantage of the weighted average cost method is that it is less accurate. If a business buys raw materials at very different prices, the weighted average will not adequately reflect the lowest or highest cost. This could result in the company setting the price of goods too low, resulting in a loss of money on sales that used the components bought at the high price. Theoretically, sales of goods produced by cheaper supply batches will compensate for this loss, but this is not always the case.
When do you use weighted averages?
One scenario in which it is useful to use the weighted average method is when a single event can have several positive or negative outcomes, but the magnitude of the positive or negative outcome is variable.
Weighted averages can be subjective. Each number in a set must have a weight. How to assign weights is usually an individual decision. Two people with the same dataset may assign weights quite differently, resulting in two different weighted averages. As typical averages do not include subjective weights, they cannot be biased in the same way.
How to calculate a weighted average?
To calculate weighted averages, you need to start with a set of numbers. Weighted averages are often used to calculate grades for a class, so provide a set of grades that looks something like this.
When you have a set of numbers, you have to assign a weight to each one. The list of tasks includes homework, tests and exams. You can make a table with grades and type of assignment, for example:
The syllabus states that homework is assessed at 25% of the final grade, quizzes at 35% and exams at 40%. The next step is to multiply each grade by the appropriate weighting.
Finally, sum the results and divide them by the sum of the weights to find the final weighted average.
25% + 28,7% + 24,5% + 23,75% + 40% + 25% + 21% + 28,8% = 216,75%
0,25 + 0,35 + 0,35 + 0,25 + 0,4 + 0,25 + 0,35 + 0,4 = 2,6
216,75% / 2,6 = 83,365%
How do I use Excel to find a weighted average?
One of the most significant disadvantages of using weighted averages is that the calculations can be complicated. But it is easy to calculate in Excel.
Start by creating two columns, one containing each number and the other containing the weight of each number. Then use the SUMPRODUCT function to multiply each number by its weight and sum the results.
Then use the SUM function to find the sum of all weights. Finally, divide the SUM of the numbers by the AMOUNT of the weights to find the weighted average.