Looking to see if random sample is uniform or not I've been tracking data and I am looking to see if it is truly uniformly random. The scenario is there can be a grid of 35 colour tiles with 5 different colours (Blue, Green, Purple, Red and Yellow). So in theory over time you should see an average of 7 tiles per each colour. I have collected a sample size of 112 grids and here is the average of each colour:
B - 7.053571
G - 7.098214
P - 6.633929
R - 7.223214
Y - 6.991071
Is the sample size large enough? I'm curious to why purple is coming up so low but need to know if statistically if it is random or not? 
Any help would be greatly appreciated.
Regards,
Paul
 A: You have seen 112*35 = 3920 colors.  The expected frequency of each color is then 784.  You can use a Chi-square test to see if the colors are randomly distributed in your sample.
You saw 790 Blue, 795 Green, 743 Purple, 809 Red and 783 Yellow.
To calculate your Chi-Square statistic you sum the squared difference between the observed frequencies and the expected frequencies and divide it by the expected frequency.  
So, Chi-Square = (36 + 121 + 1681 + 625 + 1)/784 = 3.1429
We have 4 degrees of freedom (number of colors - 1).
Using a Chi-Square table we get a value of 0.5342
This means that if the colors were randomly distributed then then the probability of us receiving a Chi-Square statistic as large or larger than the one we did would be 53.42%
If the null hypothesis is that the colours are randomly distributed, then your p-value for this test would be 0.5342 which means you would nprobably not reject the null hypothesis.
Just to add, in terms of sample size, your sample is plenty big enough.  A rule of thumb that I have read is that the expected frequency should not be less than 5, which clearly at 784 we are larger than.
