Data Science and AI :: Weighted Mean
Introduction
Hi everyone, I am Bindeshwar from Post Network Academy. In the last video, I explained the concept of mean and its properties. Today, we’ll dive into the topic of the weighted mean.
What is Weighted Mean?
As the name suggests, the weighted mean assigns different weights to each observation. This can be based on the frequency or importance of the observations.
Example
Consider the following observations:
2 (weight 4)
4 (weight 3)
5 (weight 2)
6 (weight 3)
Formula
The formula for calculating the weighted mean is:
\[
\bar{x}_w = \frac{\sum_{i=1}^{K} w_i \cdot x_i}{\sum_{i=1}^{K} w_i}
\]
where \( w_i \) is the weight and \( x_i \) is the observation.
Calculation
For the given weights and observations:
\( \bar{x}_w = \frac{(4 \cdot 2) + (3 \cdot 4) + (2 \cdot 5) + (3 \cdot 6)}{4 + 3 + 2 + 3} \)
Breaking it down:
\( 4 \cdot 2 = 8 \)
\( 3 \cdot 4 = 12 \)
\( 2 \cdot 5 = 10 \)
\( 3 \cdot 6 = 18 \)
Sum of weights: \( 4 + 3 + 2 + 3 = 12 \)
Total: \( 8 + 12 + 10 + 18 = 48 \)
Therefore, the weighted mean is:
\[
\bar{x}_w = \frac{48}{12} = 4
\]
Video
Conclusion
This is how you calculate the weighted mean. I hope you found this explanation helpful. In the next video, I’ll cover more topics related to data science.