Difference Between Simple average and Weighted average

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.

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Simple average vs. Weighted average

The 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.

Simple average vs. Weighted average

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 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

Parameters of ComparisonSimple averageWeighted average
Basic DefinitionThe 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) / nWeighted Average = ∑(xiwi) / ∑wi
ConditionsJust 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 caseThere 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 indicationThe 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.

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 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.

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.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.

2. Outliners and absolute values impact the simple average, but neither the extreme value nor the outliners affect the weighted average.

References

1. https://ieeexplore.ieee.org/abstract/document/906120/

2. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5287121/

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