How to get a number of probability distributions "averaged"?

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Let us say I have 'n' vectors of data of unequal lengths. All of these vectors are similar (range, etc., see example below), and can be fitted into a specific probability distribution. How can we average out these distributions? Does it make sense? If yes, how do I go about programming it ?

For example:- for n=2, for data1 of 400 samples, I get normal distribution with range 1 to 5, and mean 3 and standard deviation 0.75.

for data2 of 500 samples, I get normal distribution with range 0.95 to 5.2, and mean 3.05 and standard deviation 0.78.

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