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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

A2 初級

# 標準偏差 (Standard Deviation)

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