How To Calculate The Standard Deviation

which of the following is not a property of the standard deviation? This is a topic that many people are looking for. star-trek-voyager.net is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, star-trek-voyager.net would like to introduce to you How To Calculate The Standard Deviation. Following along are instructions in the video below:

“This video. I m going to talk about how to calculate the standard deviation of of a set of numbers. Quick and simple. So.

The first thing you want to is calculate the mean so x. Bar represents. The mean of the sample. And the mean is basically the sum of the numbers divided by the size of the sample.

So we re gonna add up the five numbers that we have 82 plus 93 plus 98 plus 89 plus 88. And since we have 5 numbers we are going to divide this by 5. So 82 plus 93 plus 98. Plus 89.

Plus 88. That gives us a sum of 450. Now let s divide that by 5 45. Divided by 5 is 9.

And if we add a 0. That gives us an average of 90. So that is our sample mean now the formula that we re going to use to calculate the standard deviation is this formula so we re going to take the difference of each x value. And the mean and then we re going to square those differences and take the sum of those squares.

And then we re gonna divide. It by n minus 1. So let me show you how to do that so the first number is 82..

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We re going to subtract that from the mean. Which is 90 and then square it the next number is 93. We re gonna subtract it from the mean and then square the mean is 90 and then it s going to be 98 minus 90. And then we re gonna keep doing this until it s finished so n is 5 and minus 1 is going to be 5 minus 1 or 4.

Now let s do this one step at a time 82 minus 90 is negative. 8. So this is gonna be negative. 8 squared.

But once you square it the negative sign won t matter and then it s gonna be plus 3. Squared 98. 98. 89.

Minus 90 is negative 1 and so forth and then divided by 4. So go ahead and type this in so. We have. 8.

Squared. Plus. 3. Squared.

Plus. 8. Squared..

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Plus. 1. Squared. Plus.

2. Squared. So that adds up to 142 divide. That by 4 and then take the square root of that used all and so you should get a standard deviation of five point nine five eight.

So this is the answer now let s try another example. But one way four more numbers. Involve so go ahead and try this calculate the standard deviation of the numbers. I forgot the s.

There the numbers shown in the table below feel free to pause. The video and try it so let s begin by calculating the sample mean so let s take the sum of all the numbers so we have 76 plus 84. Plus 69 plus 92. And so forth so we re gonna take the sum of all of these numbers and then we re gonna divide it by the size of the sample so a next sample we have 10 numbers so n is 10 76 plus 84 plus 69 plus 82 plus 58 plus 89 and this is just a lot of numbers let me try that again.

I think i did that wrong so the some of those ten numbers is 800 and if we divide it by ten this will give us an average of 80. So that s the sample mean now let s calculate the standard deviation of the sample. So let s use the same form of that we used earlier so it s gonna be the first number 76 minus. The mean.

Which is 80 and then squared and then it s gonna be the next one which is 84 minus. The mean and then don t forget to square. It and then we need to do this for all of the numbers..

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So the last one is gonna be 77. 82. Squared and then divided by n minus. One so we have ten numbers.

So this is gonna be ten minus. One now if you want to show all of your work. Without having to do so much right in his we could do so notice that we need to take the difference between each number and the mean the difference between 76 and 80 is negative four. But when you square a negative four.

It s going to be the same as square and positive four. So we can simply write it as 4 squared. The difference between 84 and 80 is also four so that s going to be plus. Another 4 squared.

69. Is 11 units away from 80. The next number 92. That s 12 units away from 80 and then 58.

If you do 80 minus. 58 that s a difference of. 22 and then 89 minus 80000. Civ.

9. So you need to take the squared differences of each number with the mean 73 minus 80s. A of 797 minus 80 is 1785 minus 80 is 577 minus 80th street well negative..

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3. But we ll make it positive 10 minus 1. Is 9. So now it s gonna be easier to calculate it so.

4. Squared plus. 4. Squared plus.

11. Squared plus. 12. Squared.

And so forth. Once you add all of the the squared differences. You should get 1234. So we re going to divide that number by 9 and then take the square root of the result.

So the standard deviation for this problem is 11 point. 7 nine. So now you know how to calculate the standard deviation of a set of numbers. So that s it for this video thanks for watching.

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