Hoeffding's Inequality is a piece of math that is used to calculate how far a true, underlying, statistic of a population could deviate from some observed value collected from an IID sample under a given confidence interval.

The confidence interval

The expected value (E[x])

Variable range width

The x axis lower and upper limits

number of samples >= log(2/confidence interval)/(2*deviation from expected value^2)

The number of samples you have

confidence interval = 2*e^(-2*number of samples*deviation from expected value^2)