About Weighted Mean
When certain data points are weighted more heavily than others, the weighted mean is a sort of average that helps contribute equally to the final mean. When data is related with a population, it is most typically employed in statistics. The weighted mean equals the arithmetic mean if the data is weighted the same throughout the whole set.
The weighted mean is a sort of mean that is derived by multiplying the weight connected with a specific event or outcome by the quantitative outcome associated with that event or outcome, and then adding the results together. In other words, the weighted mean is determined when some values are more important than others.
Weighted Mean Definition
The weighted mean is calculated by dividing the sum of the product of weights and quantities by the sum of weights. The weighted mean is a concept that is frequently used in accounting to assign different weights based on time or priority.
How to Calculate the Weighted Mean?
We use the arithmetic mean to get the average for a set of values that are equally weighted. Where the total number of elements in the set is divided by the sum of the values. When one of the variables has more weight than the others, the weighted mean is calculated. These two easy steps can be used to compute it:
- Multiply the numbers in the set by the weights.
- Add the results.
However, in some cases, one data collection is more significant than the others. Each of the values (x)n has a weight (w)n assigned to it. The general formula for calculating the weighted mean is as follows:
Weighted mean = Σ(w)n (x?)n/Σ(w)n
where,
- x? = the mean value of the set of given data.
- w = corresponding weight for each observation.
The weight mean is calculated using the following basic steps:
Step 1: Add together all of the weighted values.
Step 2: Multiply the weighted values with the quantities in the data set in
Step 3: Combine the values acquired in steps 2 and 3.
Step 4: Subtract the result from the number obtained in step 1.
Weighted Mean Formula
By assigning weights to the quantities, the weighted mean formula aids in the calculation of their mean. Weights are assigned to quantities based on their importance level. Variables x1, x2, x3...xn, and their weights w1, w2, w3...wn are all included in the weighted mean formula below. The weighted mean represents the sum of all the accessible quantities, and it is similar to the average. The individual quantities and the weighted mean have the same units.
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