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  • Hi. It's Mr. Andersen and in this video I'm going to talk about Standard

  • Deviation. When you're collecting data in a science lab the amount of data you collect

  • is important. So is the average. But another important statistic is going to be the standard

  • deviation of your sample. And so in this video I'm going to show you what it is conceptually.

  • I'm then going to show you how to calculate standard deviation by hand and then finally

  • I'm going to show you how to calculate it using a spreadsheet. And so first of all,

  • what is it? Well to understand standard deviation you'll have to understand the normal distribution.

  • And so what does that mean? Well, it's a bell shaped curve. You might think of it like that.

  • And so in the United States most men are about 5 foot 9. In other words that's the average

  • right here. That's the mean, or in statistics that's the X bar. But there's going to be

  • a lot of men who are obviously taller than that and a lot who are shorter than that.

  • And so the standard deviation is going to measure the spread or the variation in this

  • bell shaped curve. And so basically if we were to go right over to here, this dark area

  • is going to be 1 standard deviation above and 1 standard deviation below the mean. Or

  • it's going to be below the average. And there's something cool about that. About 68% of the

  • individuals are going to be in this area. So 1 standard deviation above and below. Or

  • if we were to look at this for example, down here is two standard deviations and so 95%

  • of individuals are going to be within 2 standard deviations from that mean. And then finally

  • if we go way down here 99% of individuals are going to be within 3 standard deviations

  • of the mean. But the standard deviation is going to vary depending on the data that you

  • collect. So if we have two curves like this, so if this is one curve and then we had another

  • curve that look like this, that data plotted on the same curve, this on is going to have

  • a smaller standard deviation than this one. They're both going to have stand deviations

  • obviously. They're going to have amounts where it's 68, 95 and 99% of the people, but this

  • one down here since it's more spread out is going to have a higher standard deviation.

  • And so how do we calculate that? Well the equation is a little scary. The scary part

  • ends up being right here. So students are a little scared by that, the summation symbol.

  • But it's actually pretty straight forward. It's not that hard to calculate the standard

  • deviation. And so let me show you how to do that. And so first thing you want to do is

  • you want to have a data set. And so here's going to be our data set right here. And to

  • make this easy let's say we just have five pieces of data. 1, 2, 3, 4, and 5. So you're

  • collecting data and this is the data in your data table. And you want to figure out the

  • standard deviation of that. Well to set that up we're basically going to take the square

  • root of the summation of this divided by the degrees of freedom. So that sounds a little

  • bit scary and so let's go to the scariest part to begin with. Let's look at what's going

  • on right here underneath that square root. And so what this is, so if we go like this,

  • the summation of x minus x bar squared, basically it means for each of these data points that

  • I have we're going to have to figure out what's right here, so x minus x bar. And so the first

  • thing we have to do is figure out what the average is. So we have to figure out what

  • x bar is. Well basically if I add 1, 2, 3, 4, 5 together I get fifteen. And if I divide

  • that by n, which is the total number of data points, so in this case n equals 5. So we

  • have 5 data points over here. So if I divide 15 by 5 hopefully you can figure out an average,

  • the average is going to be 3. And so the mean is 3 or the average is 3. So what we have

  • to do is we have to calculate this value for all five of these data points. What does that

  • mean? Well right here we're going to use x and x for the first case is going to be 1.

  • So that's going to be 1 minus 3 and then we're going to square that. So what is that? 1 minus

  • 3 and we square that is going to be negative 2 and if we square that, so that's negative

  • 2 squared and if we square that that's 4. Let's go to the next one. Well this is 2 minus

  • 3 so that stays the same. So that's negative 1 squared. And so that's going to be negative

  • one squared or that's going to equal one. If we go to the next one, that's easy. That's

  • 3 minus 3 squared equals 0. And if we square 0 that's going to be 0. Go to the next one.

  • That's going to be 4 minus 3. That's going to be 1 squared or equal to 1. And then finally

  • if we go 5 minus 3, square it. That's going to be 2 squared and that's going to equal

  • four. And so if you ever see the summation sign, don't be scared by that. It's not scary

  • at all. It just means you've got to do a lot of work. So for each of these data points

  • 1 through 5 I had to calculate what was in there. And then I have to add it all up. So

  • I have to add 4 plus 1 plus 1 plus 4. And if I add all of those up I get 10. And so

  • what's going to be inside there is simply going to be 10. So let's figure out the rest

  • of my standard deviation. Standard deviation is going to be the square root, in this case

  • we've solved this as equal to 10 and then we're going to divide that by n minus 1. So

  • what's n? That's our sample size. In this case it's 5 and so we take n minus 1 and that's

  • going to equal four. And so what is our standard deviation? It's the square root of 10 divided

  • by four which is 2.5. Or if we take the standard deviation of, the square root of 2.5, that's

  • going to be something like 1.58. And so you're going to have to use a calculator to figure

  • that out. Well what does that mean? If we were to plot this data as a histogram for

  • example, this would be our standard deviation. 1.58. And so it takes awhile to figure that

  • out based on doing it by hand. And so if you want to, give it a try. And so here's a data

  • set over here and so try to calculate the standard deviation using this data set over

  • here. And try to do it by hand. I'll put the answer down in the description below the video.

  • But I would give it a try. It's worth doing once on your own. And again this is going

  • to be our formula, standard deviation and so try to do that. Try to do that by hand.

  • And so I'll wait. No, I won't wait for you to do that. Pause the video. Try to do this

  • one and I'm going to show you how to calculate this really really quickly. And so I'm going

  • to show you the spreadsheet shortcut. And so how do you do that in a spreadsheet. It's

  • pretty simple. So what I'm going to do is going to take this data and I'm going to switch

  • over here to Excel. So here's the data right here. 0, 2, 4, 5 and 7. And so I've entered

  • my data into different cells. And now I'm going to figure out the mean, just to show

  • you how easy this is. To figure out the mean I'm going to hit an = here and then I'm going

  • to just start typing. So I'm going to type in average because the spread sheet's not

  • going to use the word mean. So I type in the word average and then I select my data. I

  • hit a closed parenthesis, I hit end and it's going to give me my average with is going

  • to be 3.6. So if I wanted to know the average there it is. If I want to know the median

  • for example I could just type median and I could go down like that and so spreadsheets

  • are super simple. And so what are we looking for? We're looking for the standard deviation.

  • So how do I do that? I just hit =. I then start typing stdev, can you see how it pops

  • up right here, standard deviation, parenthesis and then I'm going to select that and then

  • I'm going to go like that. So what's the standard deviation? It's 2.7. What does that mean?

  • We had a bigger spread in the second data set then we did in the first set. A higher

  • standard deviation. And if you did it by hand it should've look something like that. So

  • that's standard deviation and I hope that's helpful.

Hi. It's Mr. Andersen and in this video I'm going to talk about Standard

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A2 初級

標準偏差 (Standard Deviation)

  • 90 13
    Wayne Lin に公開 2021 年 01 月 14 日
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