Sample mean and covariance

Imagine you have a lot of toys, and you want to know how heavy they are on average. To find out, you would add up the weight of all your toys and then divide that total by the number of toys you have. The number you get is called the "sample mean", and it tells you the average weight of your toys.

Now imagine you have two big piles of toys. You want to know how much they are alike in terms of weight. To do this, you would look at how much each toy in one pile weighs compared to its corresponding toy in the other pile. That comparison tells you how much the piles "co-vary" with each other, and that number is called the "covariance". It helps you understand how similar or different the two piles are from each other.

So basically, the sample mean is a way to find the average of a group of numbers, and the covariance is a way to compare two groups of numbers to see how similar they are.