This concept is used to calculate "weighted averages, etc."
Find the average of x and y
For example.
You have variables x and y. You are asked to find the average of these variables.
We are asked to find the average of these variables.
How would you find it?
$$
\frac{x+y}{2}
$$
So.
Let's assign values to x and y
x = 10
y = 100
Let's say
The average is.
$$
\frac{10+100}{2} = 55
$$
and the average is $$ \frac{10+100}{2} = 55 $$.
Let's think about it with a real example.
Let's think of this as a test score.
If there are 4 people who got a score of 10 and 2 people who got a score of 100, how should we calculate the total number of people who got a score of 100?
If we do it normally, we divide the total score by the total number of people.
$$
\frac{10+10+10+10+10+100+100}{6} = 40
$$
and the average score will be 40.
Let's simply represent the above example.
This is fine, but can't we express it more simply?
There are only 10's and 100's on the test.
Therefore.
$$
\frac{10n+100m}{n+m} = 40
$$
can be expressed as $$ \frac{10n+100m}{n+m} = 40 $$.
By the way, n is the number of people with 10 points and m is the number of people with 100 points.
What is the weight?
The n,m are called weights, (when calculating the average).
n is the weight for 10 points and m is the weight for 100 points.
The reason why we say "weight" is because this value has a physical meaning: `the position of the center of gravity when a weight of n grams is placed at the 10 position and a weight of m grams at the 100 position on the number line.
This is the point where 10 and 100 are endowed with m:n.
In this case, it is only for two points, but the same calculation is performed for more points.
Like the average, it can be applied to expected value as well.
The term "weight" has meaning for concepts similar to the average, such as expected value.
For example.
If the probability of winning 100 is 3/10 and the probability of winning 500 is 1/10
The expected value is
"the average value calculated by weighting 0 yen by 6/10, 100 yen by 3/10, and 500 yen by 1/10.
It can be said to be
Also, the expected value calculation for continuous probability
$$
∫xf(x)dx
$$
in the
density function $f(x)$ is also sometimes called "weight" in the same sense.