The mean is the average of the sample data, while standard deviation is the average of the differences of each data to the mean. This could only be valid if there is a normal distribution. This distribution pertains to a bell-shaped frequency graph. However, in particle size distribution, the frequency of the sizes is rarely concentrated on the medium or middle size. It may be skewed to the left or skewed to the right. So, the mean and standard deviation is not a good measure for this type of distribution.
