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Standard Deviation - YouTube
Channel: Bozeman Science
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hi it's mr. Andersen and in this video
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I'm going to talk about standard
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deviation when you're collecting data in
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a science lab the amount of data you
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collect is important so is the average
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but another important statistic is going
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to be the standard deviation of your
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sample and so in this video I'm going to
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show you what it is conceptually I'm
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then going to show you how to calculate
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standard deviation by hand and then
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finally I'm going to show you how to
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calculate it using a spreadsheet and so
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first of all what is it well to
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understand standard deviation you have
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to understand the normal distribution
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and so what does that mean well your
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it's a bell-shaped curve you might think
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of it like that
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and so in the United States most men are
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about 5 foot 9 in other words that's the
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average right here that's the mean or in
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statistics that's the x-bar but there's
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going to be a lot of men who obviously
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are taller than that and a lot who are
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shorter than that and so the standard
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deviation is going to measure the spread
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or the variation in this bell-shaped
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curve and so basically if we were to go
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right over here this dark area is going
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to be one standard deviation above and
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one standard deviation below the mean or
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it's going to be below the average and
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there's something cool about that about
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68% of the individuals are going to be
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in this area so one standard deviation
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above and below but for you to look at
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this for example down here is two
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standard deviations and so 95% of
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individuals are going to be within two
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standard deviations from that mean and
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then finally if we go way down here 99%
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of individuals are going to be within
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three standard deviations of the mean
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but the standard deviation is going to
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vary depending on the data that you
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collect and so if we had two curves like
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this so if this is one curve and then we
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had another curve that looked like this
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that data plotted up plotted on the same
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curve this one is going to have a
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smaller standard deviation than this one
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they're both going to have standard
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deviations obviously they're going to
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have amounts where it's 68 95 and 90
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percent of the people but this one down
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here since it's more spread out is going
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to have a higher standard deviation and
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so how do we calculate that well the
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equation is a little scary
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the scary part it ends up being right
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here so students are a little scared by
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that the summation symbol but it's
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actually pretty straightforward it's not
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that hard to calculate the standard
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deviation and so let me show you how to
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do that and so first thing you want to
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do is you want to have a data set so
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here's going to be our data set right
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here and to make this easy let's say we
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just have four pieces of data one two
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three four and five so you're collecting
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data and this is the data in your data
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table and you want to figure out the
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standard deviation to that well to set
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that up we're basically going to take
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the square root of the summation of this
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divided by the degrees of freedom so
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that sounds a little bit scary and so
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let's go to the scariest part to begin
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with so let's look at what's going on
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right here underneath that square root
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and so what this is so if we go like
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this the summation of x minus x-bar
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squared basically means for each of
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these data points that I have we're
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going to have to figure out what's right
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here so X minus X bar and so the first
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thing we have to do is figure out what
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the average is we have to figure out
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what X bar is well basically if I add
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one two three four five together I get
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15 and if I divide but that by n which
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is the total number of data points so in
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this case N equals five so we have five
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data points over here so if I divide 15
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by five hopefully you can figure out an
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average the average is going to be three
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and so the mean is three or the average
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is three so what we have to do is we
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have to calculate this value for all
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five of these data points what does that
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mean well right here we're going to use
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X and X for the first case is going to
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be one so that's going to be one minus
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three and then we're going to square
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that so what is that one minus three and
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we square that is going to be negative
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two and if we square that so that's
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negative two squared and if we square
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that that's four let's go to the next
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one well this is two minus three so that
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stays the same so that's negative one
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squared
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and so that's going to be negative 1
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squared or that's going to equal 1 if we
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go to the next one that's easy that's 3
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minus 3 squared equals 0 and if we
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square 0 that's going to be 0 go to the
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next one that's going to be 4 minus 3
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and so that's going to be 1 squared or
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equal to 1 and then finally if we go 5
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minus 3 square it that's going to be 2
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squared and that's going to equal 4 and
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so if you ever see the summation sign
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don't be scared by that it's not scary
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at all it just means you got to do a lot
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of work so for each of these data points
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1 through 5 I had to calculate what was
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in there and then I have to add it all
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up so I have to add 4 plus 1 plus 1 plus
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4 and if I add all those up I get 10 and
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so what's going to be inside there it's
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simply going to be 10 so let's figure
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out the rest of my standard deviation
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standard deviation is going to be the
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square root in this case we solve this
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as equal to 10 and then we're going to
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divide that by n minus 1
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so what's n that's our sample size in
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this case it's 5 and so we take n minus
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1 and that's going to equal 4 and so
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what is our standard deviation it's the
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square root of 10 divided by 4 which is
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2.5 or if we take the standard deviation
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of the square root of 2.5 that's going
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to be something like 1.5 8 and so you're
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going to have to use a calculator to
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figure that out well what does that mean
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if we were to plot this data as a
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histogram for example this would be our
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standard deviation one point five eight
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and so it takes awhile to figure that
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out based on doing it by hand and so if
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you want to give it a try and so here's
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data set over here and so try to
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calculate the standard deviation using
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this data set over here and try to do it
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by a hand I'll put the answer down in
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the description below the video but I
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would give it a try so it's worth doing
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once on your own and again this is going
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to be our formula standard deviation and
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so try to do that try to do that by hand
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and so I'll wait no I won't wait for you
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to do that pause the video try to do
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this one and I'm going to show you how
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to calculate this really really quickly
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so I'm going to show you the spread
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she shortcut and so how did how do you
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do that in a spreadsheet it's pretty
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simple so what I'm going to do is going
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to take this data and I'm going to
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switch over here to excel so here's the
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data right here zero two four five and
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seven and so I've entered my data in in
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two different cells and now I'm going to
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figure out the mean just to show you how
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easy this is to figure out the mean I'm
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going to hit it equals here and then I'm
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just going to start typing so I'm going
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to type in average because the
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spreadsheet is not going to use the word
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mean so I type in average and then I
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select my data I hit a close parenthesis
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I hit and and it's going to give me my
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average which is going to be three point
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six so if I wanted to know the average
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there it is if I wanted to know the
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median for example I could just type
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median and I could go down like that
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so spreadsheets are super simple and so
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what are we looking for we're looking
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for the standard deviation so how do I
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do that I just hit equals I then start
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typing stdev can you see how it pops up
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right here standard deviation
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parentheses then I'm going to select
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that and then I'm going to go like that
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so what's the standard deviation it's
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2.7 what does that mean we had a bigger
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spread in the second data set that we
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did in the first set a higher standard
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deviation and if you did it by hand it
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should look something like that
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so that's standard deviation and I hope
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that's helpful
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