The arithmetic mean, what we usually call the mean, is the arithmetic mean,
Suppose a student's final exam, Chinese 90, Math 85, English 90,
Average Score = (90 + 85 + 90) / 3
about = 88.3
However, if the proportion of each subject is different, such as 30% for Chinese, 40% for mathematics, and 30% for English, the average with different proportions is the weighted average
Weighted Average Score = (90 * 0.3 + 85 * 0.4 + 90 * 0.3) / (0.3 + 0.4 + 0.3)
= 88
The "weight" in the weighted average is the meaning of the weight (that is, the proportion), that is, the contribution (importance) of each number to the final average is different.
When the contribution is the same, the weighted average at this time The number is the arithmetic mean.
The weight can be set according to the needs (different environments and different needs will be different)
The formula for the weighted average is as follows:
Numerical value: [x1, ... xn]
The weight of each number: [w1, ... wn] //The
arithmetic mean of the weight can be defined by itself (it is a special weighted average): all values are added together Divide by the total number
a = (x1 + .... + xn) / n
weighted average: all values multiplied by their own weights and added and divided by the sum of the weights
b = (x1 * w1 + ... + xn * wn) / (w1 + ... + wn)
So, when the weights are all the same (and 1), the weighted mean is the same as the arithmetic mean.
Summarize:
The arithmetic mean is a special weighted mean;
The weighted mean is a generalized model of the arithmetic mean;
When the weights are the same, the arithmetic mean is equal to the weighted mean;
Reference: https://en.wikipedia.org/wiki/%E5%8A%A0%E6%AC%8A%E5%B9%B3%E5%9D%87%E6%95%B8