What is Standard Deviation?

The term “Standard Deviation” comes up quite a lot in certain types of research papers where statistics are mentioned. As a result, I have to wonder exactly what it tells us, why it is interesting, and how it works.

Thankfully the basic idea is fairly simple, so I don’t need extensive training in statistics to understand what it means. In fact, I just picked up an old copy of a statistics textbook at a second-hand book shop, and it tells me everything I need to know. (And a lot more that I probably don’t!) Read more What is Standard Deviation?

Even Powers and Odd Numbers

This is a very simple mathematical relationship I found out about recently, which I rather like (although I don’t claim to be original… it’s probably been covered millions of times before!). Here’s an example:

12 = 1
22 = 4 = 1 + 3
32 = 8 = 1 + 3 + 5
42 = 16 = 1 + 3 + 5 + 7
52 = 25 = 1 + 3 + 5 + 7 + 9

You’ll notice that the square numbers are being formed by sums of consecutive odd numbers, starting at 1. I don’t have a mathematical proof for this (although I’m sure one exists), but it appears to work for any even power. I wrote a quick computer program to try the same with the 10th power, and sure enough, it works: Read more Even Powers and Odd Numbers