[Music] hi it's Mr Anderson and in this video I'm going to talk about Standard air Standard air is one of my favorite statistics and the reason why is that it shows you how good your data is and and let me show you what I'm talking about so let's say I collect two data sets so this is data set one and this is data set two if you were to look at the data you would say well this one over here seems to show more Precision it's going to have more data and it doesn't seem to be spread out as much but if I were to graph this data so of these two data sets if I were simply to create a graph showing the mean or the average of the data both of them would be 12 and so if I had a bar graph it would look like this for both data set one and data set 2 and so you should never have a bar graph if you're using it to represent a lot of data unless it has error bars on it and so how do you figure out what the standard error is how do you make these standard error bars well let me show you um so basically I'll work through data set two and then I'll ask you to work through data set one I'll put the answer down in the description down below and so to figure out Standard air the equation is really um ingenious basically all they do is they take the standard deviation and we divide it by the square root of the sample size why is that important well what does standard deviation measure standard deviation is going to measure the spread or how far the data is spread out and so if you have a lot of spread then you're going to have a large Standard air and the other thing it uses is the sample size so the sample size is how much data are you collecting if you collect a lot of data and we're going to have a large number here then that's going to decrease my standard err likewise if I have not much data at all that's going to increase my standard err so let's get to standard deviation if you don't know how to calculate standard deviation or even what it is and how it measures spread you're going to go want to go watch a video and so here's a little link I'll put to a video I made on standard deviation so you you could simply click here or I'll put a link to the standard deviation in the uh video description down below but you want to figure out how to do standard deviation I show you how to do it by hand and then I'll show you how to use a spreadsheet to calculate standard deviation very very quickly and then what is sample size well sample size is going to be the number of trials that you do or the number of data points that you collect and so if we were to look at data set 2 there are 10 numbers over here and so that means I'm going to have a sample size of 10 and so keeping those in mind let me switch over to the spreadsheet and show you how I would figure this out so right here I'm in Excel this is going to be data set two again I'm going to show you how to do that one and then here's data set one so what I'm going to do is since I've got this column right here I'm going to first of all calculate the average of that or the mean of that if you were to type equals mean for the mean nothing will show up and that's because spreadsheets don't use the word mean they're going to use the word average so you can see that that pops up and I'm going to put a first I hit an equal sign then I'm going to write in average and then parentheses and now I'm going to tell Excel which kind of a data I want to figure out the average from I put it in parenthesis and it simply calculates for me that it's 12 now here's a quick little trick um so I've done the average for this column if I select this average and then I move my cursor down here watch how it changes so it changes from that to that and so I can click it now and then just drag that over here and Excel is smart enough that it's going to figure out oh if you want the average of this now you want the average of this column so you can see that the average is going to be the same now let me show you how to do the standard deviation if you did that by hand it takes forever and so it's really important that you use either a calculator or a spreadsheet to do this I'm going to hit equals and then I'm going to start typing stde V that's going to be standard deviation I'm going to hit a parentheses then I'm going to select the data and then I'm going to hit end parenthesis and there's my standard deviation now if we were to compare that to the standard viation of data set one so again let me do that trick I'm going to select this move this over here you can see that data set one has a much larger standard deviation that means it's going to have a greater spread in the data but I'm going to figure out the standard error of this first one so this is 825 and so how do I I'm going to remember these numbers here and then switch back and figure it out so let me write down the things that I need to know so my xar or my mean I said is going to be 12 the N or the sample size size we said is going to be 10 in data set 2 cuz I have 10 um values over here on the right and then the standard deviation that I just calculated is going to be .826 and I did that in Excel so how do I figure out the standard de or standard err so the standard err of the mean is simply going to be the standard deviation which is 826 and then I'm going to divide that by the square root of the sample size and the square root of the sample size is going to be 10 and so this is equal to 826 / the square < TK of 10 I'm going to need my calculator right here and that is going to be 3.6 and then I have to figure out so let me write that down so that's 3.16 and then uh if I take 826 / 3.16 I get 261 so 26 one is my standard error or standard error of the meat so you could figure out the standard error of the data set one remember in data set one we simply had two values 9 and 15 and so if you want to figure out the standard err of those and so you make sure you're doing that right you could do that and I'll put the values down below um but what does this all mean well let me show you why this is super important so if we go over here and look at our graph again so I just figured fur out the um standard error of data set 2 and so what that means is data set 2 my mean is 12 and so the average is 12 but I could add an error bar on the top like that and then I could add an error on the bottom and my standard err is going to be we said. 261 in other words it goes from 12 up to 12. uh 261 and then from 12 down to 12us 261 so we're going to have an error bar on each side what you could do is go figure out set one uh set one you're going to have a much larger standard deviation you're going to have a smaller sample size and so I would imagine you're going to have pretty big error bars and so what's neat about that is the bar graph now with those standard error bars is going to show me um kind of the story it's going to tell me about the data behind the mean or the data behind the average and so standard airs it's pretty straightforward it's simple you're probably going to need a spreadsheet to do it and I hope that was helpful