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50215 - ZScore normalization

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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Question by Ibrahim Mesecan.

ZScore normalization

There are several methods to put the items in the same scale. In Z-score normalization arithmetic mean is subtracted from each data item and the result is divided by the standard deviation.

where μ is the arithmetic mean and σ is the standard deviation of the sequence.

Question: Write a program that reads a sequence of numbers and then normalizes them using ZScore.

Input specification
You will be first given a number (n) the number of numbers, where 0 ≤ n ≤ 5000. Then in the following line, you will be given n integers which are between -50,000 and 50,000.

Output specification:
Show the normalized sequence with two digits precision.

Sample Input I
5
9 7 10 5 8
Sample Output I
0.62 -0.42 1.14 -1.46 0.10

Explanation: There are 5 numbers given. And, arithmetic mean μ = 7.8 and σ = 1.9235. If μ is subtracted from all the numbers and then divided by σ, we have the given sequence.



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