Reconstructing datasets

[arikel]

is it possible to reconstruct datasets from a mean and standard deviation in someone's report?

thanks!

[Dragan]

is it possible to reconstruct datasets from a mean and standard deviation in someone's report?

thanks!

No, you cannot. Theoretically, there are infinitely possible data sets (with different shapes i.e. values of skew and kurtosis) that could have the same values of mean and standard deviation.

Think of your question this way: Suppose the values of the mean and standard deviation in your report happen to be 0 and 1, respectively. How many data sets are there that could have a mean of 0 and standard deviation of 1?

Answer: Infinitely many because I can take any data set and impose a linear transformation on the data (in this case a z transformation z=(X-Mu)/Sigma) such that the data will have a mean of 0 and standard deviation of 1. And, that z transformation will leave the shape of the distribution unchanged. That is, the values of skew and kurtosis will be precisely that same - before and after the transformation.

This idea (example) is completely general to any other arbitray values of mean and standard deviation.

[Borjana]

Hi sorry i dont kno if u can help me but i have a test soon on statistics and i need desperate help.. in normal distribtutions X~N(1.3,0.15^2) how would i find the 80th percentile and what does that even mean?

[Dragan]

Hi sorry i dont kno if u can help me but i have a test soon on statistics and i need desperate help.. in normal distribtutions X~N(1.3,0.15^2) how would i find the 80th percentile and what does that even mean?

Well, if X~N(Mu=1.3,Sigma=15) then 80th percentile is X=13.9243. The interpretation is that approximately 80% of the data points fall at (or) below a score of X=13.9243.

Easily done using the standard normal curve to determine "z" by finding the value of "z" such that solved "z" yields a proportion (20%) of the normal density above that value. That is "z"=0.84162.

And, of course, subsequently using:

X=Sigma*z + Mu = 13.9423,

Mkay.

[arikel]

Thanks Dragan! Brilliantly clear response