Numerical smoothing and differentiation

Numerical smoothing and differentiation are both parts of a process of figuring out how to get information and data from numbers.

Numerical smoothing is a process of taking a group of numbers and making them smoother by looking at the patterns that emerge. This can be useful because sometimes when we look at a set of numbers, there are small, random fluctuations that make it hard to see the overall trend. Smoothing can help us get rid of these fluctuations so we can better understand what is happening over time. Imagine you're drawing a line on paper. Sometimes, if you draw it quickly, the line can look jagged and bumpy. But if you go back and smooth it out, the line looks smoother and easier to follow. That's what numerical smoothing does for numbers.

Numerical differentiation, on the other hand, is a process of figuring out how fast things are changing by using differences between the numbers. When we look at a set of numbers, we can see how much they change from one point to another. This helps us understand how quickly things are moving or changing. Imagine you're on a bicycle and you're going faster and faster. Someone asks you how fast you're going, and to answer that, you would need to know how much your speed has increased between two points in time. That's what numerical differentiation does for numbers.

Both numerical smoothing and differentiation help us make sense of big sets of numbers by allowing us to better understand the patterns within them.