How to Calculate Standard Deviation

Video Transcript

"Hi, I'm Steve Jones and I'm going to show you how to calculate standard deviation. This, which we call sigma, sigma is the symbol for standard deviation. This is a very important quantity in science and math generally as we need to very often work out how much our results are accurate, whether they're close to the result we want or whether they're further away. But the first thing we have to do is work out what we call an arithmetic mean. and the arithmetic mean x bar is x one plus x two. Now these exes are the different things we've measured. Alright, if I now do a series of readings and an experiment and I get a series of readings that look like six point one, then five point nine, then six point zero, then five point eight, then six point two, and then six point zero again. Each of these readings is slightly different, but I know that I can use this formula to get the arithmetic mean just by adding all these together and dividing by six, because there are six; one, two, three, four, five, six readings and I divide by six. So in fact the average of these, the mean of these is six. Now in this formula I need to use my reading and take from it the arithmetic mean. So, here it would be six point one minus six point zero, which is zero point one. Now here, five point nine is lower so it's actually five point nine minus six point zero, which is minus zero point one. It doesn't matter as you will see. And so on, I can go down and do the other values. These values can be inserted. And as you see here, I've got x minus x bar squared. By squaring it what I'm getting is something which removes the negative sign. So I'm going to get the positive sign all the time, then I divide by the number of objects, and finally I square root the result, which is a positive number and gives me a number, and the number is going to be around well zero point of one five. zero point one five is going to be the nominal deviation at the end of this process. So the reason for doing this is that I can say that whatever my result, if I've got a result around six, it's good to within zero point one five."