 I like if you're getting I mean if you're getting to the standard deviation you're going to do the variance right you get it's part of the it's part of the steps so notice that the variance is calculated with a sigma 2 squared and the standard deviation will often be represented by just the sigma because and we'll see that in a second so this is going to be the variance represented with the sigma squared and we're going to basically do our sum item if we're going to represent this and we're going to say i sub 1 to n so we've got x sub i which is going to represent each number in our data set we had four numbers minus mu which represents the mean and then instead of taking the absolute value of this as we did last time we're going to square it now note what that does when I square it that does what the absolute value did and that it removes the negative numbers because if I square negative numbers they will result in positive numbers if I square positive numbers also result in positive numbers so that does the same thing but it also gives us a problem where now everything is bigger it's all been squared and then I'm going to divide it by n which is the count which is similar to what we had with the average deviation so so if I look at the standard deviation we're just going to take it one step further this entire thing is right here but now we're going to take the square root of the entire thing so that's why the variance is often represented with a sigma squared whereas the standard deviation just the the sigma so everything under the square root is the same and you can kind of think well yeah I squared it now so I know I rep now I've got this large number if I reverse the squaring of it taking the square root of it in it you know in essence then you're going to get kind you think you you'd get kind of a similar point now most of the times when people look at this they say well why would you square it well because I'm getting rid of the negative numbers and you could say well why why you could have got rid of the negative numbers by just taking the absolute value and then you wouldn't have to take the square root right why why take the square root and then and then and then I mean why take the squaring of it so it can't it can't simply be is what I'm trying to say it can't simply be that the only reason to do that is to get rid of the negative numbers although it does to have that feature because you would think that taking the square root would still be easier if you were going to do that so we'll talk more about that in the future but note the squaring does have that capacity of getting rid of the negative numbers and then you take the square root and and then and then you get caught you would think kind of to a similar point but it's not exactly the same over here so you can kind of compare and contrast the intuitive which you might do with the average deviation versus the variance and the standard deviation okay so let's take a look at this then so now we have our same data set and if I did this in a table kind of format I would compare each of those data sets x by minus the mean which came out to zero so I get to the I get our same numbers because in this case the middle point happened to be zero so the distance is always going to be the same number away from that middle point in this data set and then the difference between what we did this time and last time is instead of taking the absolute value of these numbers because I end up with that problem they add up to zero that doesn't help me right so what I want to do instead of taking the absolute value I'll square them so if I square all of them six squared is 36 right so so now I get up to a much larger number than when I just took you know six and I made an absolute value of six right I just made them all positive so six squared is 36 four squared is 16 four squared positive four squared 16 and positive six squared 36 so all the negatives get removed in that process but then when I sum these up 36 plus 16 plus 16 plus 36 I come out to 104 versus over here which I came up to simply 20 and so then I can say okay that's basically this bit x sub i minus mu squared and so then I'm gonna I summed those up and then I'm gonna divide by the count or in so now I'm gonna divide by n similar to what we did before the count one two three four of them represented here and so 104 divided by four is going to give us the variance which is represented by sigma square 26 and then I can take the square root of that taking the square root of 26 gets us to the 510 now I know if you're doing this on a computer and you pull out your trusty calculator you can change your calculator type to something like a scientific calculator so you have you know some more of these calculation tools so so for example if I took this negative six up top and I said the negative six I'm gonna say negative and then six there it is and then I've got my squared item here so I could say squared is going to be 36 right so that's you can calculate that in your calculator and then down here we've got the 104 obviously 104 divided by four gives us our 26 and then I want to take the square root of the 26 and that is here so we get to about 5.09