Weighted Mean Vs Arithmetic Mean
Weighted mean and the arithmetic mean are explained using a table for better visualization.
Let’s consider the following data set:
| Value | Weight |
|---|---|
| 10 | 2 |
| 20 | 3 |
| 30 | 5 |
Arithmetic Mean Calculation:
{Arithmetic Mean} = {Sum of Values}\{Number of Values}}
Sum of Values = (10×1) + (20×1) +(30×1) = 10+20+30 = 60
Number of Values=3
Arithmetic Mean = 60/3 = 20
Weighted Mean Calculation:
Weighted Mean = (w1×q1 + w2×q2 + w3×q3……………….+ wn×qn )/ (w1+ w2+ w3 +…….wn)
Sum of (Values × Weights) = (10×2) + (20×3) + (30×5) = 20 + 60 + 150 = 230
Sum of Weights = 2+3+5 = 10
Weighted Mean = 230/10 = 23
| Value | Weight | Value x Weight |
|---|---|---|
| 10 | 2 | 20 |
| 20 | 3 | 60 |
| 30 | 5 | 150 |
So, the arithmetic mean for this data set is 20, while the weighted mean is 23. This shows how the weights affect the outcome, pulling the mean higher due to the emphasis placed on the larger values.
Article Related to Weighted Mean:
Weighted Mean Formula
Mean is also called average in Mathematics which denotes the sum of all given quantities divided by the number of quantities. The arithmetic mean is important in statistics. For example, Let’s say there are only two quantities involved, the arithmetic mean is obtained simply by adding the quantities and dividing by 2.
Table of Content
- What is Weighted Mean?
- Weighted Mean Formula
- How to Calculate Weighted Mean?
- Weighted Mean Vs Arithmetic Mean
- Arithmetic Mean Calculation:
- Weighted Mean Calculation:
- Weighted Mean Examples