**Standard Deviation** can be used to determine how precise a series of calculations are in relation to one another.

Mean Evaluation

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## Mean Evaluation

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So here we're gonna say that our standard deviation measures how close data results are in relation to the mean or average value. So basically the smaller standard deviation is the more precise, your measurements will be in relation to the mean or average value. So here the formula for standard deviation is s which stands for standard deviation equals the square root. And here we have the summation of our measurements minus our average squared divided by n minus one. In terms of this equation, we're going to say here that X I here represents an individual measurement that we're undertaking in terms of our dataset, we're going to say that our average or mean value is represented by X. With the line on top, variance is just our standard deviation squared. Later on, when we get more into statistical analysis will see that the f test has a close relationship to the variants of our calculations. Next we have and which represents our numbers of measurements and and -1 represents our degree of freedom. Finally, we have our relative standard deviation also called R coefficient of variation. That is just our standard deviation divided by our meaner average value, times 100. So at some point we're gonna run into using one of these um variables in terms of the standard deviation equation. So just remember the smaller standard deviation is the more precise all your measurements are within your data set. Now your measurements can be precise but that doesn't necessarily mean they will be accurate. Remember accuracy is how close you are to a true value. Your measurements themselves may be close to one another, but still far off from the actual true value. So the accuracy may not be good. Now that you've known the basics of standard deviation, we'll take a look at the example left below, so click on the next video and see how I approach this question, which deals with standard deviation.

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So here it says data below gives the volume detained biochemist from the use of a pie pod, determine the standard deviation. So we have our measurements of 24.9 mL 25 mL 24.8 millimeters 24.6 twice. And then 24.3 mL. Alright, so what we're gonna do first is we're going to fill out this chart. We have each of our measurements which represents our volumes here. So that's 24.9, 25, 24.8, 24.6, 24.6 and then 24.3 Here we would get the mean or average. Remember the average would just be each one of these numbers added up together then divided by the total number of measurements. Okay, so you would do 24.9 plus 25.0 plus 24.8 as well as the others and divided by the total number of measurements, which is six, That will give you at the end 24.7, so that represents our mean or average value. Now here we're gonna do the difference from the mean. So each one of these measurements will subtract from the mean. So that gives me point to here Gives Me .3, we get 0.1 so on and so forth. So the difference here will give me negative 0.1 negative 0.1 and negative 0.4. Then we do the difference from the mean squared. So basically we're squaring each one of these. Okay? And then Okay, and squaring each of them. This one gives us .04 0.9 0.1 0.1 .01 and .16. So now we would add them all up together. This summation value here means basically I am adding up all of these totals together. Okay, so that's all it means I'm just adding up all of them together And when I add them all up together it gives me .32. So now we need to finally figure out our standard deviations. Remember your standard deviation equal square root? The summation of each measurement - the average and then you square that divided by N -1. We found out that this top portion is .32 And is the number of measurements which is six volumes that we had initially -1. So then here inside that give me .064. So your standard deviation will be .252982. Since each one of my volumes here has three sig figs, we just go with 36 things at the end. So my standard deviation here is 360.253. Again, remember the smaller standard deviation is the more precise or closeness Each of your measurements have to one another. Again, this does not necessarily mean that they are accurate. We have to compare these values here to some true value. Okay, so from there then we'd be able to determine if it's accurate or not. All we can tell at this point is that our standard deviation is pretty small. Um The numbers are very close to another, so there is some precision involved.