hello AP biology students this is going to be our sixth section of the precontent in unit zero and in this section we're going to talk about something called Standard air of the mean to start out this section I like to show my students this bar graph usually during the first week of school we test some product whether it be like toilet paper or soap and to graph their data my students usually produce a bar graph that looks like this and I ask them how confident are you that brand B is the best I try to actually put a dollar value like how much are you willing to spend that b is the best I asked are you willing to bet $5 $10 $100 $1,000 and we typically get various answers I then say this is the actual data each one of these dots along the bar graph represents one data point of that set of data and the bar graphs represent the averages of that data side note I did just make and randomly place these points along the bar graph but then I asked my students how confident are you now that brand B is the best and their answers usually change they go well I'm not that conf anymore then I showed them this graph and I say okay what if this was the data how confident are you now and the students usually probably like oh yeah I'm a lot more confident i' bet a lot more money then I go back to this graph and say well you're showing me this graph how do I know what the data Behind These averages actually tells me or in other words how do I know if I'm looking at this graph or this graph when I'm just looking at the averages and I think it helps them click like oh yeah these are incomplete graphs I need something else to show where the the data is and that's where standard error of the mean comes in this is a measure of how a stample average is going to represent the actual populations mean so basically we have this data for the whole population but we can't logistically take data from the whole population so we take a sample from just a random sampling and how does that represent the total population that is what standard error measures after we calculate standard error of the mean we use something called error bars to represent this value these are called error bars and they go above and below where the average sits for a bar graph and these ER bars or bar-headed lines represent the variability or the variation in the data remember how before we talked about within group variation and between group variation these error bars are going to help us represent that within and between group variation so this is why we talked about variation and standard deviation before we got to these things called Stand error bars now before I go on I just want to remind everyone that this is for a high school level AP Biology class there is a lot that goes into error bar standard ER the mean standard deviation and just statistics in general and it can get really difficult to understand all of these attributes but what I'm trying to focus on for this section is just what you need to know for an AP bio class when comparing two sets of data you can see the bar graphs here if these error bars overlap the data is not significant how I like to explain this to students stud is that these airor bars show the variation within the average for that set of data in other words if we took this average again it could be between anywhere between these two points let's say tomorrow we come in and we run the same exact test that test could show me an average here or an average here same for this set of data if we did the test tomorrow the average could be all the way down here and all the way up here this is just because there is a lot of variation in that data so let's say on one day the average comes up to here and the average goes up to here that looks like data set B is actually larger than data set a but on the next day the average could be here for a and down here for B which makes it look like a is going to be larger than B that just shows there's a lot of variation in the data and it's not significant to say that a is larger than b when air bars don't overlap that means the data is significant so again you can see there is no overlapping between data set a and data set B so no matter when we do this average you can see that this average is always going to be higher than this average but those are the two main Concepts students need to understand is when there's no overlap the data is significant and when there's overlap the data is not significant so the next question is how do we graph these error bars well we graph something called two standard errors of the mean or semem so again you can see we have our bar graph with an average what's going to happen is we're going to make an error bar going in the positive direction and an airor bar going in the negative Direction so you can see our margins of errror one goes in the positive one goes in the negative and we graph two of them so you can see there are two standard errors going in the positive direction and two standard errors going in the negative Direction now you might ask why do we do two standard errors for biology and specifically an AP Biology class we go for something called a 95% confidence interval and if you remember back to our standard deviation section that's because two standard errors of the mean give us a 95% confidence rating now again there's a lot more that goes into this if you are Ed I implore you take an AP Stat class but just basically we're just graphing two standard deviations with us two two standard errors now when looking at these error bars you might have noticed that some of the error bars are very large while some are very small smaller error bars indicate more significant data generally this is usually due to two reasons one is they have a large data sample size and two there's small variation in the data larger error bars on the other hand indicate less significant data generally this could be due to reasons or both of these reasons they had small data sample sizes or large variation in their data now the last thing we have to understand with standard error is how to calculate it to calculate standard error of the mean all you have to do is take the standard deviation which we already calculated and divide it by the square root of n or the number of data points again this is a lot easier when you actually show a problem some you give you an practice problem remember our practice problem from before we had data points 1 2 3 4 5 our standard deviation was 1 .58 the number of data points is five and our average was three so all we have to do is plug in numbers we take the standard deviation and divid it by the square root of n which is 5 and if we plug those numbers in we're going to calculate that the standard error of the mean is 0.7 and yes it's that easy it's just plugging in two numbers and figuring out the standard error now remember when we graph this standard error the mean we have to graph two of them in the positive direction and two of them in the negative Direction so again we have our data our average three you can see that we graphed it here and our standard error of the mean is 0.7 so what we're going to do is we're going to go up 7 and go up another 7 we're going to make our bar-headed line and we're going to do the same for the negative direction we're going to go down 0.7 and down another 0.7 and put our bar-headed line that's going to show us the standard error of the mean for this data you can see that we have a bar-headed line in the positive direction of 1.4 and a bar-headed line in the negative direction of 1.7 and that's all you have to do to graph standard error the mean it's important to understand though that each data set each average is going to have a different standard error of the mean so if I was graphing another bar graph it wouldn't have the same standard of the mean it's going to have a different standard error based on its data