Suppose I have the accuracies of 10 runs for an algorithm X, I can directly find the average and STD for these 10 runs, but if I have only the average and STD, how can I find the performances of these 10 runs ( vice versa )?
You just can't. 10 runs are 10 degrees of freedom. You are fixing two by imposing the mean and the std, so you still have 8 degrees of freedom to go. There are infinite combinations that will yield the same mean and std.
One thing that you can do is to use Tchebyschev's inequality to bound the probability that you get large values, but I am afraid there is not much more you can do.
I concur with the answer given above by Giovanni Stea sir. However, I would like to add that though you cannot find the exact values for the 10 instances, you can compute the percentile information based on the type of distribution your data follows.
You may refer the following link for having an idea of computing percentiles for the data with normal distribution.
http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Probability/BS704_Probability10.html
Hope it helps!
I would like to thank Deeksha Arya and Giovanni Stea for their logically answer. however, I found the following website that try to solve the same problem using estimating values.
https://www.extendoffice.com/documents/excel/2472-excel-random-number-mean-standard-deviation.html
hope it helps.
Best regards
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