Why this distribution of data is not normal ?
The following 20 random numbers were generated using a programming language's rand() function.
(0.448997214,0.726326642,0.301226192,0.113561565,0.675253205,0.630750208,0.072041345,0.974423096,0.851475029
0.379741908,0.959473489,0.149021966,0.792596568,0.353847243,0.38587524,0.774162247,0.890049562,0.665856554
0.339205262,0.989926791).
A histogram of the above 20 data points is shown below.
There are three ranges of equal width where the frequency (no of observations) are different (9,7,4). As per the definition of randomly generated numbers , these numbers are in the range [0,1] and when N numbers are generated the frequency of occurrence of these random numbers should be identical across a certain number of intervals. What explains the discrepancy observed above (See Histogram).
A. There are not a lot of observation points. A distribution tends to normality only for a large number of observations as per the central limit theorem.
B. The random number generator being used generates pseudo random numbers as it uses a mathematical function to generate random numbers.
C. True randomness can only occur in Nature such as observations of frequency of sound in the universe etc.,
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1 solution
All these could be reasons why a perfectly normally distributed set of random numbers is not being generated. A. There are not a lot of observation points. A distribution tends to normality only for a large number of observations as per the central limit theorem.
B. The random number generator being used generates pseudo random numbers as it uses a mathematical function to generate random numbers.
C. True randomness can only occur in Nature such as observations of frequency of sound in the universe etc.