Algorithms for calculating variance
Have you ever played a game where you have to find the average (mean) of a bunch of numbers? For example, let's say we have to find the average of 3, 4, and 5. We add them up (3+4+5 = 12) and then divide by how many numbers there are (3). So the average is 4.
When we talk about variance, we want to know how much the numbers (or data) are spread out from the average. In other words, we want to know how different each number is from the average. To calculate variance, we use a formula that involves subtracting each number from the average, squaring that difference, adding up all those squared differences, and then dividing by how many numbers there are.
Let's use the same example of 3, 4, and 5 to calculate variance. First, we find the average like we did before (add up and divide by 3). The average is 4.
Next, we subtract each number from the average and square the differences:
3 - 4 = -1, (-1)^2 = 1
4 - 4 = 0, 0^2 = 0
5 - 4 = 1, 1^2 = 1
Now we add up all those squared differences: 1 + 0 + 1 = 2
Finally, we divide by how many numbers there are (3): 2/3 = 0.67
So the variance of 3, 4, and 5 is 0.67.
In more complicated situations with a lot of numbers or data, we use a computer algorithm to do all the subtracting, squaring, adding, and dividing for us. But the idea is the same as the example above - we want to know how different each number is from the average, and then how much all those differences vary from each other.
When we talk about variance, we want to know how much the numbers (or data) are spread out from the average. In other words, we want to know how different each number is from the average. To calculate variance, we use a formula that involves subtracting each number from the average, squaring that difference, adding up all those squared differences, and then dividing by how many numbers there are.
Let's use the same example of 3, 4, and 5 to calculate variance. First, we find the average like we did before (add up and divide by 3). The average is 4.
Next, we subtract each number from the average and square the differences:
3 - 4 = -1, (-1)^2 = 1
4 - 4 = 0, 0^2 = 0
5 - 4 = 1, 1^2 = 1
Now we add up all those squared differences: 1 + 0 + 1 = 2
Finally, we divide by how many numbers there are (3): 2/3 = 0.67
So the variance of 3, 4, and 5 is 0.67.
In more complicated situations with a lot of numbers or data, we use a computer algorithm to do all the subtracting, squaring, adding, and dividing for us. But the idea is the same as the example above - we want to know how different each number is from the average, and then how much all those differences vary from each other.
Related topics others have asked about: