 two times and then we have how many twos happened one hundred and seventy one hundred and sixty threes one hundred and sixty four fours one forty nine fives and one seventy five sixes and we can see that those add up to a thousand which makes sense because we rolled it a thousand times that's kind of our check figure the difference then this is what we expected to happen this is what actually happened so there's a difference of fifteen it's pretty close but not exact a difference of three a difference of seven on the positive side a difference of three a difference of eighteen a difference of eight and so on so then if i was to plot this i can say this is the actual outcome right so the expected was a straight line but the actual outcome is not exactly a straight line but if i was to try to predict what's going to happen in the future it's useful for me to be able to use a function of basically just the straight line right i'm going to you if i'm gonna say what's gonna happen in the future well this looks like it can be approximated pretty closely with the straight line so that's why the straight that's why that's going to give us some predictive power about what will happen in the future if i wasn't able to do that if i was to say hey look this doesn't look like it conforms to anything it's just that the numbers are coming up randomly which could very well happen in different circumstances some data sets might not be able to be represented with some kind of of line or approximating a formula and if that's the case then then it's gonna be a lot more complex for us to to use past data to project future data into the future but if we're saying hey look this looks like it approximates some kind of actual curve in this case a straight line then we can use the formula to help give us some predictive power of what's gonna happen in the future so notice that this histogram up top i made with a bar chart and we could make the make the histogram as well with a histogram in excel if we do it with a histogram the histogram in excel is going to try to give us a top and bottom number but you can see there's a there's one it's one number distance apart so we so you can use either of those formula those uh... charts to in essence get get the same uh... result so if you want to check that out in excel will have that and excel now in excel if also you wanted to run this experience this experiment multiple times and say okay that's pretty close right here to the straight line what if i did it four times uh... then and uh... i can run multiple experiments and say okay who are all of them going to come out similar similar so we rolled once again we did the the random number generator between one through six as if we rolled the dice a thousand times four times right so again this is what what i apparently they used to do for for uh... that in the universities you know if you worked in there they had you know people just roll in dice all day uh... and they're part of the union job and stuff but now we have the computer doing that you know it took a long time but that but now the dice rollers are out of there and we just jet we generated with the computer now so then if we if we made our our histograms this way you could see again it it's approximating a straight line this is the first uh... results this is then the second results not exactly the same of course because there's randomness in it but you can see it still kind of approximates the straight line here's the third one of a thousand rules so they're all different they all you know approximate basically that straight line and the idea if you think about the sampling concept would be that if i was to roll this an infinite amount of times which would be the entire population then it would in essence be you know a straight line representation uh... meaning you would expect the outcome to be one over six right for each uh... role times in an infinite number of times right uh... but because we have a sample of of the data it's not going to it's not going to come out perfect but we can approximate it uh... with our formula and so that's the easiest kind of formula to approximate right it's a straight line we can see we can see that now obviously if we can do a similar thing with curves which will talk about in future presentations representing the data with a more complex formula but still a formula so that we can make predictions uh... with with uh... with a formula then that would be great as well will get into some of those in future presentations