How can I determine if a set of numbers is truly random based on a histogram?

[abcdmichelle]

1. The problem statement

If i generate a list of 300 random numbers in excel, each number between 1-50 for example, and i plot the frequency that each number comes in a histogram, how can i tell, looking at the histogram, if the numbers are really random? is there a certain distribution the histogram will follow?

The Attempt at a Solution

I would assume that every number between 1 and 50 would have the same probability of coming up so the histogram would have more or less even bars. however, doesn't a poisson or gaussian distribution represent random events, and then wouldn't the histogram have to be a bell shaped curve?

can someone please help me!?
looking at the histogram, how can i tell if the numbers are actually random?

 

[cosmo123]

It sounds like a Chi-square test is suitable for this. I think you use the fact that if it was random, you would expect each number 1-50 to come up 6 times, so the distribution should just be rectangular.

 

[HallsofIvy]

You can't tell by just looking. The chi-square test, as cosmo123 said, can test give a probability that numbers were generated randomly but remember it is possible (though extremely unlikely) that a randomly generated set of numbers could be all the same number! That is, there is no way of knowing for sure if a given set of numbers was randomly generated. Any set of numbers could be generated randomly.