To obtain some (at least approximate) statistics about a random variable, you need to assume some form . of distribution or create an (even implicitly) approximate one. When you have some samples, you can estimate the mean and std. deviation using usual formulas. They are not the true statistics, albeit data estimates, which are assumed to be close the true values. You actually did this for your samples, i.e. you estimated the mean and deviation of your data from your samples. These are point estimates and don't give much hint about the underlying distribution of your statistics. In order to get statistics about your estimated statistics, you need to obtain several of them, e.g. for getting std of your mean estimate, you need to have several mean estimates. But, your data is constant, and you have only one mean estimate here. Same problem arises when we ask about the deviation of your estimated deviation, or the percentage you ask for.
One way to create several of these estimates is to use bootstrapping. You resample your data with replacement and obtain several realizations, e.g. $[12,9,10],[10,9,12],[10,10,9],...$, record the mean of each of these, redo the same for the second set, calculate the percentage. After all, you'll have several percentages and you can directly estimate the deviation you ask for. But note that, this is a computational methodology.