Updated June 29, 2023
Difference Between Average vs Weighted Average
Two of the most used statistics in the world are an average and weighted average. Both averages and weighted averages have their merits and demerits and have their proper usage in particular scenarios. Coming to the definition, a simple average is nothing but adding all the observations under a sample and dividing the same by several observations in a given sample. For example, if we want to calculate an average of the sample given, say 9, 10, 15, 29, 35, the same can be done by adding all of them, i.e. (9+10+15+29+35) / 5 = 19.6.
When calculating a weighted average, each observation in the data set is multiplied by or assigned weight before being summed to derive a single average value. This process entails assigning a weight to each quantity being averaged to determine its relative importance. The weightings ensure that items with similar values contribute more significantly to the average.
Head To Head Comparison Between Average vs Weighted Average (Infographics)
Below is the top 7 difference between Average vs Weighted Average:
Key Differences Between Average vs Weighted Average
Let us discuss some of the major differences between Average vs Weighted Average.
- The key difference between an average vs weighted average is that a simple average is nothing but adding up all the observation values and dividing the same by the total number of observations to calculate the average. In contrast, the weighted average is an average where each observation value will have a frequency assigned or specific weight to calculate the average.
- Average finds the middle value, termed as central tendency, whereas weighted averages find the average, which is tilted towards more number of observations.
- Arithmetic means median and mode are the types of central tendency, whereas the weighted average is not a type of central tendency.
- Observations are always assumed to be equally weighted when using a simple average. In contrast, with a weighted average, each observation is assigned a unique and different value.
- Outliers or extreme values can impact the simple average, whereas the weighted average remains unaffected by such extreme values or outliers.
- Weighted averages find extensive accounting, finance, and portfolio value calculation usage. On the other hand, the simple average has broader applications but is limited by its susceptibility to extreme values. In practical life, the calculation of the simple average is often supported by complementary averages such as the weighted average or simple moving average.
- The weighted average has one big limitation: the weights assigned can be subjective, affecting its calculation. In contrast, there is no such case in the calculation of simple.
Average vs Weighted Average Comparison Table
Let’s look at the top 7 Comparisons between Average vs Weighted Average.
|Basis of Comparison||Average||Weighted Average|
|Basic Definition||The average is calculated by summing the observations given in the sample and dividing that sum by the number of observations in the sample.||A weighted average is the type of average in which every observation in the given data set will be assigned weight before the summation to a sole average value.|
|Formula||Average = ∑(x) / n
Where ∑(x) is the summation of all observations
n is the number of observations
|Weighted Average = ∑(xiwi) / ∑wi
Where xi is the ith observation
wi is the weight of the ith observation
∑(xiwi) is the summation of the product of xi and wi
∑wi is the summation of the weights.
|Conditions||This average will only work when all of the observations are weighted equally.||In a weighted average, each observation has a frequency assigned to it or a specific weight.|
|Use case||There are no specific conditions where the simple average has to be applied. Still, if other conditions are met, other averages are appropriate to use as a weighted average, moving average, etc.||
|Result indication||The average is utilized to determine and generalize the middle value, earning the name “central tendency” for this purpose.||The weighted average accurately represents the range where most observations fall and tend to lean toward that range. This approach finds extensive use in the accounting field.|
|Advantage||A simple average advantage is its simplicity of calculation and understanding.||A weighted average is justified by its unbiasedness towards the middle value and the assigned average value where most observations lie. Additionally, it remains unaffected by outliers or extreme values.|
|Disadvantage||The simple average is affected by outliers.||The weighted average becomes a little complicated to understand when several observations increase, and further, the weight assigned is of subjective matter and hence can be adjusted per user discretion.|
People use the simple average in mathematical equations, whereas they utilize and apply the weighted average in their daily or routine activities, such as finance. The simple average is a given data set’s main and key representation.
In contrast, one must evaluate the weighted average first to arrive at a specific solution for a particular problem. One can use arithmetic formulas such as finding the median to solve the average of a given data set or observations. The components are assigned weights based on their values to obtain a specific answer in the weighted average.
The weighted average is the one that shows up in many areas of finance besides the buying price of the shares, including inventory accounting, portfolio returns, and valuation. For inventory accounting, the weighted average value of inventory accounts for ups and downs in commodity prices, for example. At the same time, FIFO and LIFO methods give more importance to timing than value. When evaluating whether the company’s shares are properly priced, investors will use the weighted average cost of capital to discount a company’s future cash flows.
This has been a guide to the top difference between Average vs Weighted Average. Here we also discuss the Average vs Weighted Average key differences with infographics and comparison table. You may also have a look at the following articles to learn more –