It is not entirely clear on what you are trying to measure. Standard deviation is typically used to measure confidence (and report errors, etc.) in a statistical calculation. And so to divide one quantity (range) by another (standard deviation of price) is kind of like dividing a number by a color. Consider some other indicators, like Bollinger Bands, as mentioned, where you have the average value +/- n*std. deviations, which is a valid way to present a statistical measurement.
About using standard deviation to represent the probability of all values (even those not measured yet) falling within certain percentages of the mean, this is only valid for normal distributions (and these are ~68%, 95%, and 99.7%, not the other mentioned values), as was indicated. Stock-price distributions are not normally-distributed (they have fat tails), and so this doesn't apply. You can still calculate a variance (and standard deviation), but you can't make the same confidence claims as before.
About using standard deviation to represent the probability of all values (even those not measured yet) falling within certain percentages of the mean, this is only valid for normal distributions (and these are ~68%, 95%, and 99.7%, not the other mentioned values), as was indicated. Stock-price distributions are not normally-distributed (they have fat tails), and so this doesn't apply. You can still calculate a variance (and standard deviation), but you can't make the same confidence claims as before.
