stats Q

[iwantanewcomputer]

all from the same population, i have 3 sets of data sigma and mean, but not the actual data. are these enough to find the sigma and mean of whole pop?

 

[Random Variable]

Do you mean that you have three separate sets of sample data? The most you can do is create confidence intervals.

 

[Whisper]

Originally posted by: Random Variable
Do you mean that you have three separate sets of sample data? The most you can do is create confidence intervals.

Yep. The sample statistics you have are all approximations of the population statistics, which in most cases are impossible to ever actually obtain. The larger the number of samples, the more precise (in theory) your approximations become, but they still are never equal to the exact population data.

Edit: I should also mention that you'd want to be sure that the sample statistics did indeed come from the same population, usually via something such as a t-test or an F-test

 

[Paperdoc]

As Whisper says, you can obtain a better ESTIMATE of the Mean and Std Dev for the full population, but you cannot know those stats exactly. However, you are still missing some data. In order to calculate new estimates of Mean and Std Dev., you need to know the number of observations in each of the three samples. IF you have that data also, then:

Grand Mean is just weighted average of the three means - weighted, that is, by their observation numbers, n.

GM = [M1 x n1 + M2 x n2 + M3 x n3] / [n1 + n2 + n3]

To do the Pooled Estimate of Standard Deviation, it's rather like taking it back to the Sums of Squares used to get the Variance and its root, the Std Dev. We undo the square roots and add the sums of squares, then plug that back into a new square root, in essence.

Pooled SD = Sqr Root of{[(SD1)^2 x (n1-1) + (SD2)^2 x (n2-1) + (SD3)^2 x (n3-1)] / [n1 + n2 + n3 - 3]}

Note that the denominator inside the square root has a "-3" at the end, not "-1", because the number of "degrees of freedom" involved in pooling three separate samples is THREE less than the total number of observations.

That gives you the new estimates of the two statistics. With them, as another suggested, you could also calculate Confidence Intervals for those estimates (which will be narrower because you now have a larger number of observations included). Remember, though, to adjust the Degrees of Freedom as above in using the t-tables to find the required t-value.