The essence of the problem may be that your distribution is not a normal distribution which a standard deviation assumes. Your distribution is likely left skewed, so you need to transform your set into a normal distribution first by picking a suitable transform function, this process is called distribution fitting. One such function candidate in your case might be a mirrored log transform. Once your set satisfies a normality test you may then take the standard deviation. Then to use your 1$\sigma$ or 2$\sigma$ values you must transform them back into your original data space using the inverse of your transform function. I'm thinking this is what your professor was hinting at.

The essence of the problem may be that your distribution is not a normal distribution which a standard deviation assumes. Your distribution is likely left skewed, so you need to transform your set into a normal distribution first by picking a suitable transform function, this process is called transformation to normality. One such function candidate in your case might be a mirrored log transform. Once your set satisfies a normality test you may then take the standard deviation. Then to use your 1$\sigma$ or 2$\sigma$ values you must transform them back into your original data space using the inverse of your transform function. I'm thinking this is what your professor was hinting at.