A simple average and a weighted average are Some of the world’s largest most commonly used stats. Both weighted and averages have benefits and inconveniences, as well as specific applications. To put it another way, a simple average is nothing more than adding all of the data in a sample and dividing that total by the number of occurrences in that sample.
Simple average vs. Weighted average
The main difference between Simple average and Weighted average is that a simple average is obtained by adding or divided the total number of observations into all observation values, but a weighted average is calculated by assigning a frequency or particular weight to each observation value.
A set of observations’ simple average is calculated by multiplying the total of the individual observations by the number of observations in the set. The teacher wants to know what their average score is. The simple average is 83.8, as calculated by SA = (82 + 78 + 83 + 91 + 85) / 5 = 83.8.
The most common applications of weighted averages are in the fields of accounting, finance, and portfolio valuation. The simple average, on the other hand, has a wide range of applications, and its computation is always aided in practice by supplementary averages such as weighted averages or simple moving averages, due to its inability to be impacted by extreme values.
Comparison Table Between Simple average and Weighted average
| Parameters of Comparison | Simple average | Weighted average |
| Basic Definition | The Simple Average combining all sample observations and splitting it up by the number of observations in the sample, a mean is calculated. | A weighted average is some kind of averaging whereby each observation in the data collection is weighted before being combined to produce one assessment completed. |
| Formula | Average = ∑(x) / n | Weighted Average = ∑(xiwi) / ∑wi |
| Conditions | Just because all of the data are evenly weighted will this average operate. | Each observation in a weighted average is allocated a frequency or a specified weight. |
| Use case | There are no specified circumstances in which the basic average must be used. | When you have a set of observations, each of which has a frequency associated with it. |
| Result indication | The average is sometimes called the middle trend since it is employed to identify and generalize the interquartile range. | The weighted average shows, and will rely on, the majority of the observations. And is used in accounting most often. |
What is a Simple average?
The major advantage of the simple average is how simple it is to calculate. However, one disadvantage of the simple average approach is that it may not accurately reflect an average, especially if the items in the collection have different significance.
As a result, a simple average is a useful approach for calculating the average of a group of variables with equal relevance. The use of a weighted average may be more accurate in other instances.
It is a technique for inventory valuation or delivery cost computation in which the average unit cost is determined by multiplying the total of these unit costs by the number of receivings, even if the inventory products have varying unit costs. The following is an example of the Simple Average Method. In this example, the total unit cost received from the 1st to the 24th is 900 yen, and the receiving time is four, implying a receiving unit cost of 225 yen on average. Multiplying the average unit cost (225 yen) by the balance yields the inventory valuation (9,000 yen) (40).
What is the Weighted average?
The weighted average has one major flaw: the weights assigned might be subjective, which has an impact on the computation. In the case of basic calculations, however, this is not the situation. A weighted average is a computation that considers the relative value of the integers in a data collection. Each value in the data set is multiplied by a preset weight first before the final computation is done when computing a weighted average.
A weighted average could be more precise than a basic average, which assigns the same weight to all values in a data collection.
The most common use of a weighted average is to equalize the frequency of values in a data collection. For example, a survey may collect sufficient responses from every age category to be scientifically accurate, but the 18-34 age group may have fewer respondents than the other age groups according to their population share. The questionnaire survey can weigh the findings of the 18-34 age group to ensure that their perspectives are well-reflected.
Values in a data collection may, however, be weighted for reasons other than frequency of occurrence. If participants in a ballet class are assessed on the skill, attendance, and etiquette, the skill grade may carry more weight than the other elements.
Main Differences Between Simple average and Weighted average
1. The advantage of a simple average is that it is easy to compute and comprehend. But A weighted average is employed because it is unbiased towards the middle value and given average value, which is where the majority of the observations are located.
2. The disadvantage of a simple average Outliers have an impact on the basic average. But When the number of observations rises, the weight assigned gets harder to comprehend, and the weight assigned is a subjective matter that may be modified at the discretion of the user.
3. The median and fashion means are core trend types however the weighted average would not be a main trend
4.Observations are typically believed to be similarly consideredwhen using a simple average. In the case of a weighted average, on the other hand, separate value is assigned for each observation, a unique value.
5. Outliners and absolute values impact the simple average, but neither the extreme value nor the outliners affect the weighted average.
Conclusion
In the mathematical formulae, the simple average is employed. The weighted average,On either hand, it are being used and used in daily or routine living tasks such as economics. A data set’s main and most important representation is the simple average.
The weighted average, on the other hand, will need to be analyzed first to arrive at a specific solution for a given problem. Arithmetic formulae such as determining the median may be used to calculate the average of a given data set or collection of observations, but in the weighted average, the components must be assigned the weight of value to arrive at a certain result.
References
1. https://ieeexplore.ieee.org/abstract/document/906120/
2. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5287121/