Think about it this way. If you know the population variance, there would be no need to calculate an estimate using the sample variance. If you don't know the population variance, then you can estimate it using your sample to be an unbiased estimator.
It is mentioned on page 58 of the specification qualifications.pearson.com/content/dam/pdf/A%20Level/Mathematics/2017/specification-and-sample-assesment/a-level-l3-mathematics-specification-issue4.pdf , and I would make sure you know the difference, but I feel that it is unlikely that you would end up using it as the variance of the population should be given in a question for a sample means hypothesis test.
s_x is the sample standard deviation, sigma_x is the population standard deviation. So if I had some numbers: 2, 3, 5, 7, 8, 8, 9, 9 Then the standard deviation of these numbers is sigma_x = 2.55 In the majority of situations when you're dealing with statistics, these numbers would represent a SAMPLE of a larger population, rather than being the whole population by themselves. So we would often be more interested in having an unbiased estimator for the population standard deviation, which is s_x = 2.72.
Speaking from a statistician's viewpoint, the likelihood of you having the whole of a population's data is very slim. In the majority of real-world scenarios, you have access to the data of a sample, from which you can infer the population standard deviation by using s (dividing by n-1). Which exam board are you using?
@@user-yg5ol8fj6v For OCR MEI, they're much more on the ball when considering the population and sample standard deviations. Essentially, if it is clear a sample has been taken in the context of the problem (as it will most likely be), use the sample standard deviation
I don't quite understand why you divide by n-1. Doesn't dividing by a smaller number mean that the sample standard deviation will be bigger than the population standard deviation? But here you implied it would be smaller.
If I take a sample, like 101, 103, 103, 105, 106, 110, then the standard deviation of these numbers (dividing by n=6) we get 2.867... However, this is likely to be too small a value to represent the population the sample came from, as it is unlikely the sample picked up many (if any) of the extreme values. So the sample standard deviation (dividing by n=6-1=5) is 3.141.
![A-Level Maths: L3-14 [Data: OCR MEI and the Standard Deviation]](http://i.ytimg.com/vi/TJfltKEi30o/mqdefault.jpg)
![A-Level Maths: L3-14 [Data: OCR MEI and the Standard Deviation]](/img/tr.png)
![A-Level Maths: L3-11 [Data: Introducing the Variance and Standard Deviation]](http://i.ytimg.com/vi/eZB1TdtO7zQ/mqdefault.jpg)
![A-Level Maths: L3-16 [Data: The Standard Deviation from Summary Statistics]](http://i.ytimg.com/vi/sQaXCLbCGtk/mqdefault.jpg)
![A-Level Maths: O1-01 [Hypothesis Testing: An Introduction]](/img/n.gif)
You are an amazing teacher
In exam questions how would you know wheater to use the equation for population variance or unbiased population variance (sample variance)?
Think about it this way.
If you know the population variance, there would be no need to calculate an estimate using the sample variance.
If you don't know the population variance, then you can estimate it using your sample to be an unbiased estimator.
Is sample standard deviation in the edexcel spec cause it's not in my applied book?
It is mentioned on page 58 of the specification qualifications.pearson.com/content/dam/pdf/A%20Level/Mathematics/2017/specification-and-sample-assesment/a-level-l3-mathematics-specification-issue4.pdf , and I would make sure you know the difference, but I feel that it is unlikely that you would end up using it as the variance of the population should be given in a question for a sample means hypothesis test.
You mention that sigma_x and S_x are both the sample standard deviation, I don't really understand the difference if so?
s_x is the sample standard deviation,
sigma_x is the population standard deviation.
So if I had some numbers:
2, 3, 5, 7, 8, 8, 9, 9
Then the standard deviation of these numbers is sigma_x = 2.55
In the majority of situations when you're dealing with statistics, these numbers would represent a SAMPLE of a larger population, rather than being the whole population by themselves. So we would often be more interested in having an unbiased estimator for the population standard deviation, which is s_x = 2.72.
How would you know whether to divide by n or n-1 if the question doesn’t make it clear whether it’s a population or sample?
Speaking from a statistician's viewpoint, the likelihood of you having the whole of a population's data is very slim. In the majority of real-world scenarios, you have access to the data of a sample, from which you can infer the population standard deviation by using s (dividing by n-1). Which exam board are you using?
@@TLMathsocr-Mei
@@user-yg5ol8fj6v For OCR MEI, they're much more on the ball when considering the population and sample standard deviations. Essentially, if it is clear a sample has been taken in the context of the problem (as it will most likely be), use the sample standard deviation
Is this for Edexcel? Can’t find it on the specification
its aqa i think
I don't quite understand why you divide by n-1. Doesn't dividing by a smaller number mean that the sample standard deviation will be bigger than the population standard deviation? But here you implied it would be smaller.
If I take a sample, like 101, 103, 103, 105, 106, 110, then the standard deviation of these numbers (dividing by n=6) we get 2.867...
However, this is likely to be too small a value to represent the population the sample came from, as it is unlikely the sample picked up many (if any) of the extreme values.
So the sample standard deviation (dividing by n=6-1=5) is 3.141.