That tells you, look, this isĭefinitely a less-dispersed data set then that there. Less-dispersed data set is a lot smaller. Right, this is 10/5, which is equal to 2. And what is this equal to? All of that over 5. To- 8 minus 10 is negative 2 squared, is positive 4. Divided by- we have 1, 2, 3, 4, 5 squaredĭifferences.
#Youtube standard deviation in excel graph plus
Me scroll up a little bit- squared plus 12 minusġ0 squared. Is going to be equal to 8 minus 10 squared plus 9 minusġ0 squared plus 10 minus 10 squared plus 11 minus 10- let So let me scroll over a littleīit so we have some real estate, although I'm Variance of this less-dispersed data set. And let's compare it to thisĭata set over here. And what do we have here? 400 plus 100 is 500, plusĪnother 500 is 1000. 10 minus 10 squared, that's justĠ squared, which is 0. That, the mean, square it, take the average of those.
Of these numbers, of the squared distances. Them up, and then dividing by that number I'm finding the differenceīetween every data point and the mean, squaring them, summing So this is the squaredĭifferences between each number and the mean. The 20- squared plus 30 minus 10 squared. The middle 10 right there- plus 20 minus 10- that's Minus 10, minus the mean- this is the mean this is thatġ0 right there- squared plus 10 minus 10 squared- that's So I just found the differenceįrom that first data point to the mean and squared it. I know that sounds veryĬomplicated, but when I actually calculate it, you're Your mean, square them, and then take the average But anyway, the definition ofĪ variance is you literally take each of these data points,įind the difference between those data points and Letter actually is the symbol for standard deviation. Literally this sigma, this Greek letter, squared. We're not just sampling, taking a subset, of the data. This is all of the data for our whole population, that So the symbol for the variance-Īnd we're going to deal with the population Often, but it has a very close relationship To see the standard deviation in this video. See used most often is called the variance. With the exact same range where still, based on how thingsĪre bunched up, it could still have very differentĭistributions of where the numbers lie. This guy has a much larger range, so that tells me this Number, 12, minus the smallest number, which is 8, whichĪ pretty good measure of dispersion. Largest and the smallest number is 40, so we have a range Is equal to 40, which tells us that the difference between the Number, which is 30 in our example, and from that, you Often, but it's kind of a very simple way of understanding howįar is the spread between the largest and the Kind of the most simple way, is the range. Ways we can measure dispersion, or how farĪway we are from the center, on average. Our mean than these guys are from this mean. Set right here is more disperse, right? These guys are further away from Even the closer ones are stillġ0 away and these guys are 20 away from 10. Here, these numbers areįurther away from 10. But when you look at these twoĭata sets, one thing might pop out at you. This number, you'd say, oh, maybe these sets are very Numbers and divide by 5, you get 10, some of these numbersĪnd divide by 5, you get 10 as well. Numbers and divide by 5 or when you take the sum of these Of these data sets have the exact same arithmetic mean. Or if you don't want to worryĪbout the word population or sample and all of that, both It, 8 plus 12 is 20, 9 plus 11 is another 20, so Of this data set? 8 plus 9 plus 10 plus 11 plusġ2, all of that over 5. With that 10, 20 plus 30 is 50 divided by 5, it's And what is this equal to? That negative 10 cancels out Negative 10 plus 0 plus 10 plus 20 plus 30 over- we haveįive data points- over 5.
The arithmetic mean of this data set right here, it is But if you are going to goįurther in statistics, I just want to make thatĬlarification. Samples of it, and you're going to try to estimate With, as you see, the population measuresįancy words. This is the entire population of our data. Statistics, you're going to understand the differenceīetween a population and a sample.
Now let's calculate theĪrithmetic mean for both of these data sets. Let's say I have negativeġ0, 0, 10, 20 and 30. Video is to expand that a little bit to understand About different ways to represent the central tendency
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