High variance and standard deviation can tell us a few things about a data set. For one, it can tell us how spread out the data is. If the data is more spread out, then the variance will be higher. Additionally, high variance and standard deviation can tell us how much variation there is within a data set. If there is more variation, then the standard deviation will be higher. Finally, high variance and standard deviation can tell us if a data set is symmetrical or not. If the data is not symmetrical, then the skewness will be greater than 0.