I've got a table with 59 different values for my response variable, with different amounts of number of observations for each one of them (from 1 to 5e5, so that I observed the least frequent value once, and over 5e5 times the most frequent). This follows a normal/Gauss distribution for which I've already calculated mean, median, mode, variance and standard deviation. I've got around 5.8 million observations on this dataset.
The mean is 64.833 while the mode and median are both 65, but I found out that 44% of the observations are higher than 65 and 48% of them are lower (8% of the observations have the value of 65). My standard deviation (for a mean of 64.833) is 5.305.
Getting to the point, I want to know how significant is this difference (those 4%), considering my standard deviation. How can I calculate that? If it's significant at say, 5 or 10% and, if not, the lowest p-value at which that would actually be significant?
I'm currently thinking on using a Hypthotesis with 64.833 as my sample mean (x) against 65 as the population mean (u), as
H0: x=u H1: x!=u
My problem here is what I should use as 's' (standard deviation with 65 or 64.833 as mean?) and what I should be using as 'n' (the 5.8 million observations in the whole dataset?).
Would that work, calculating z with those values? X as 64.833, u as 65, s as 5,305 (my standard deviation with 64.833 as mean) and n as 5.8 million (my sample size that lead me to 64.833 as mean)?
Using that, I got z=-75.505, which got me a p-value of 0.00001... but I don't know if that should be it. It seems that due to the high n, pretty much anything would be significant, so I'm not sure if I should be using 5.8 million as my n or not...