 so on and and so forth so okay so notice that that number is similar but not exactly the same as what we what we got over here usually we're going to get something a little bit larger if i was to do it using the average deviation calculation versus uh taking the standard deviation we also get that pit stop along the road uh along the way which is the variance that's why it's represented again as the sigma squared and then we take the square root to get down to the standard deviation now also note at this point in time we're talking about the popular the data as though it's the entire population you have a slight difference to the formula when you're talking about the a sample so we'll talk about those differences more in future presentations if we have a sample versus the entire population uh this but excel you can also you know calculate these using excel formulas and this one is calculated using the excel formula for uh the variance and standard deviation for the population these two are using excel formulas to calculate for uh the sample so again we'll talk about the sample more in a future presentation now note obviously it's nice to be in excel and just simply put the function in place to say give me the variance give me the standard deviation and i can basically add these to my set of numbers but it's also useful to kind of go through this table sometimes because then you actually do get more of a visual representation of the data set you know to some extent and you might get a better understanding of what is being said by these numbers down here also remember that again these numbers we'll talk more about them in future presentations but they can seem more abstract than when we talk about simply the mean or the average uh of of a data set and sometimes it's useful to to compare multiple data sets and we'll talk more about that in uh future presentations now this is so now i'm just want to touch back on the question of why we would use this variance and standard deviation which seems more complex than this and we saw again most people will say well why do you square the data to get rid of the negatives well why don't i just take the absolute value instead that would be easier well one reason mathematically that you can argue for using the more complex standard deviation rather than the average deviation is that if I was to pick any other middle point it gives me a unique number in other words if i if i chose for example in our data set instead of to use the mean as the middle point but i want to look at the distance from from point number one so i use one instead of the mean and then i do everything else the same right i take the difference from that point number one and i get my differences now these differences are not going to add up to zero anymore because i'm not looking at the differences from the middle point i'm looking at the differences from just a point that i picked one and then if i was to take the absolute value of those numbers then i'd still come out to 20 right i still come out to 20 and then if i do the rest i take the 20 and i divide it by four i still come out to five so notice i don't i don't have like a unique number here when i pick the mean as the middle point as opposed to when i pick some other number when i use the average deviation so if i did the same thing using two as my as my number instead of the mean of zero i used point number two and i looked at the difference between every point in my data set and point number two which i just chose randomly again it won't add up to zero but if i take the absolute value of them i come out to 20 and i still get five and then if i do it one more time just to hammer the point home if i used three then i still come out to 20 and i get five whereas if i did that same calculation using the standard deviation and variance here's my numbers i picked point number one instead of the mean i get my same differences but then i'm going to square them and i come out to 108 that 108 is is going to be different than the 104 i came out with when i use the mean as the middle point and so that of course will result in a difference when i divide that 108 divided by four you get a different number which would be kind of representative of the variance except we used a different middle point and then you'd get 520 so now the 520 is different than the 510 that we got to when we used the middle point so that's that's one reason that you could you could say that we use you get a unique note you're going to get a unique number if i used point number two then then again the same thing applies and if i if i added up i get up to to 120 and then my end result comes out to 548 which is not the same number as we had when we used the middle point of zero so that's so that's just an argument because that comes up a lot when you're trying to kind of explain the standard deviation why you would square it and take the square root and and so it gives you a it gives you a unique value is another reason that you can you could say that could be useful right