Difference Between Average vs Weighted Average
Two of the most used statistics in the world are an average and weighted average. Both averages vs weighted average have their own merits and demerits and have their proper usage at particular scenarios. Coming to the definition, a simple average is nothing but the addition of all the observations under 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. A weighted average is the type of average in which every observation in the data set given will be multiplied by or assigned weight before summing them to a sole average value. In this process, every quantity that is to be averaged will be assigned a weight that shall determine the relative importance of every quantity. Weightings are the equivalent that is having the most of the like items with a similar value involved in 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 average vs weighted average is that simple average is nothing but simply adding up all the observation values and dividing the same by the total number of observations to calculate the average whereas the weighted average is an average where each observation value will have a frequency assigned or specific weight to it to calculate the average.
- Average finds the middle value, and hence it is termed as central tendency whereas weighted averages find the average which is tilted towards more number of observations lie.
- Arithmetic means median and mode are the types of central tendency, whereas the weighted average is not a type of central tendency.
- To use a simple average, it is always assumed that observations are equally weighted. In contrast, in the case of weighted average, each observation will be assigned a different value, and which shall be a unique value.
- The simple average is affected by outliners or the extreme values, whereas the weighted average is not affected by the extreme value or the outliners.
- Weighted averages are mostly used in the field of accounting, finance, or portfolio value calculation. In contrast, the simple average has general applications, and due to its limitation of getting affected by extreme value, its calculation is always supported by using complementary average like a weighted average or simple moving averages in practical life.
- The weighted average has one big limitation that the weights assigned can be of subjective matter which affects 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 the summation of the observations given in the sample and dividing that summation by several observations in the sample. | A weighted average is the type of average in which every observation in the given set of data 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, however, if other conditions are met, then other averages are appropriate to use as a weighted average, moving average, etc. |
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| Result indication | The average is used to find the middle value and generalize the same, hence it is also called as the central tendency. | The weighted average will depict where most of the observations fall in, and it will tilt towards that and is mostly used in the accounting field. |
| Advantage | A simple average advantage is its simplicity to calculate and understand. | A weighted average is used due to its unbiasedness towards middle value and assigned average value where most of the observations lie within. Further, it is unaffected by outliners or extreme values. |
| Disadvantage | The simple average is affected by outliers. | Weighted average becomes a little complicated to understand when several observations increases and further the weight assign are of subjective matter and hence can be adjusted per user discretion. |
Conclusion
The simple average is used in the mathematical equations. In contrast, the weighted average will be used and applied in the daily or routine activities of a person’s life, like in the field of finance. The simple average is the main and key representation of a given data set.
In contrast, the weighted average will need to be evaluated first to arrive at a certain solution for a certain specific problem. One can solve the average of a given data set or given observations by using arithmetic formulas such as finding the median, whereas, in the weighted average, the components shall be given the weight of value to arrive in a particular answer.
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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 the 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.
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