Test to determine whether a huge series of integers is random or there is a pattern?

Question

I have a series of integers in which some integers occur more than others. I want to know if there is a test to determine whether these integers are randomly distributed or some integers occur more than others due to some inherent property of the data being collected? The integers are in the range of 0-9 only

I want a test which can say that there is a statistically significant difference between the frequency of the integers. For example:

1,9,8,5,0,3....5000 such numbers

0-9%

1-11%

.

.

.

Is there a significant difference between the occurrence of the integers or it is just random.

Edit: The data series has more than 5000 observations. I am only concerned about the frequency.

Answer 1

If you are only concerned about the frequency, then a simple computer program which goes through all the integers and counts the frequency of each will suffice. Once you have the frequency table, you can do further analysis if required.

(From a frequency table, you can calculate the mean, median, standard deviation, and mode of the data, and see whether it looks like a normal distribution, etc.)