Total sum of squares

Imagine you have a bunch of toys, and you want to know how much space they would take up if you put them all together. You put them in a big pile and measure the distance from the bottom of the pile to the top. The total sum of squares is a bit like this - but instead of toys, we're measuring something called variation.

Variation is a fancy word that describes how different some numbers are from each other, or from an average number. Just like some toys might be big or small, some numbers might be far away from an average or close to it. The total sum of squares helps us measure how much variation there is in a group of numbers.

To find the total sum of squares, we need to do a few steps. First, we need to find the average number in our group. This is like finding the middle toy in our pile - it's the number that's right in between all the others.

Next, we need to subtract the average from each number and then square the result. This is like figuring out how far each toy is from the middle one, and then squaring that distance. We do this for every number in the group.

Finally, we add up all the squared distances. This is like stacking all the toys on top of each other and measuring the distance from the bottom to the top of the pile. The result is the total sum of squares.

So, if we have a group of numbers and we want to know how much variation there is between them, we use the total sum of squares to help us measure it. Just like stacking toys, we stack the squared distances between each number and the average, and add them up to find the total variation.