 over the top of an N so there we have it so you can see this is similar to what we did before and that we're going to take each of our data points we had four data points and we're going to subtract them from the mean represented by mu which in our case was zero but this time we're going to square them so that's so that's going to be something we that's a little bit different than last time and then dividing it over the number which is in so that's going to be our variance calculations I'm going to say all right let's insert that now this is going to make more sense when we then do the next step to go from the variance to the standard deviation which we're we're going to take like the square root so in essence we like square it and then we take the square root of it you know so so which kind of negates to some degree kind of like the squaring right so it's a little bit different than what we did before which we just said let's just take the absolute value of it so we don't end up with the negative numbers that will net out to zero in this case we're going to square it which has a similar kind of characteristic that it's it's not gonna because when we square it we're not going to get the negative numbers so that does something similar to the absolute value but obviously it also increases the the value of the numbers and then we're going to divide it by in alright so let's go home tab font group we'll make this orange let's increase the size of it a bit and so that looks good alright and then we're gonna get we're gonna do another one which is going to be the standard deviation for the population standard deviation for the population let's make this header formatting home tab font group black and white okay so this is going to be much the same as this this here except that we're going to take the square root of the entire thing so we'll put the whole thing under a square root for example and that's why it's going to be represented not with a sigma squared but simply a a sigma so so because we're gonna you know we're gonna take the square root remove the remove the squared here and take the square root okay so and then let's go to the insert tab and just draw it again so I'm gonna say make another equation see if I can write this oh hold on a second not that that's not what I want to let's do this one and let's see if we can write it again and so I'll just do it real quick here okay so I basically wrote the exact same thing except I don't have a squared on the sigma and then I'm just gonna add the new thing I'm gonna put I'm gonna try to put this whole thing under a square root symbol like so and so there we have it so if we were to remove the square root we would in essence have that variance that we looked at last time which is we're gonna take each data point minus the mean and then we're gonna square it which has the property of removing all of the negative numbers therefore we don't need to do the absolute divided by the count the number of N and then because we squared it you can kind of think about it while we squared it so what if I then take the absolute value of it one of the things that that will do is it's going to it's going to remove the negative numbers because when we squared it we got negative numbers and then we can absolute it which kind of negates to some degree the squaring and and so now we've come up to kind of a similar thing that we would have but not exactly similar that's gonna be one of the points when we did the average here so let's go ahead and insert that so we're gonna bring that down here so let's pull this down under here let's and what's my size this was came out to be 16 let's make this 16 and let's make it orange so you could see this is kind of similar to what we did with our intuitive calculation which was taking each point minus the mean absolute value not squaring it right but we took the absolute value to get rid of the negatives divided by two versus this where we're taking each item minus the mean and then squaring it removing so we don't have to do the absolute value but now we've squared it divided by n and then in essence taking the square root alright so what's the different let's see let's do the actual calculation and look at our data set so I'm gonna copy my data set over here let's just copy this column and so I'm gonna see if I can copy just this let's just copy that data set and put it over here let's make a skinny V put in my cursor between V and and W making it skinny and paste it right there so it's not in a table even though it looks like a table because I only copied part of the table so let's go to the insert tab up top tables and make a table out of it and there we have it alright so then I'm gonna do the same starting point we're gonna have the mean the same the same top part I'm just making the numerator here in essence so we take the mean which is equal to the same thing we calculated before zero which is simply the average of our data so we just took that zero is taking the average of the data which is you know summing them up and dividing by four and then I'm gonna double click on this number I want to make it absolute so I'm selecting F4 in the keyboard dollar sign before the D and the one so that each of these numbers are pulling from the same cell and then I'm gonna take the difference again difference same thing we did before this is going to be equal to the six minus the zero so there's our difference from the mean which of course are the same numbers in this case but wouldn't always be that because we picked the mean to be zero this is where we get something different we're not going to take the absolute value but we're going to square each of those differences so the way you do that is you say equals I'm going to point to that number and you have a carrot if you're going to take to the power of something and that's on shift six on the keyboard so there's the carrot taking it to the power of two or squaring it so we're gonna say enter so now we've squared all of them I'm gonna add a total column at the bottom now so we can do that by going to the table design and totals now if I sum up the data if I add up all my data and I just take take the I could take the average by the way if I take the average that's where our zero comes from and if I count my data here I could count the data there's four of them right and then I can take the sum of the differences which is always going to add up to zero because we're comparing everything to the middle point or the mean and then we've got the squared amount instead of the absolute value so before we had 20 because we just took the absolute value and now we've got of course a bigger number of 104 all right so now let's take out