Question

Why is it important to look at dispersion? Why is standard deviation a better measure of dispersion than the range?

Answer 1

While measures of central tendency are used to estimate "normal" values of a data set, measures of dispersion are important for describing the spread of the data, or its variation around a central value. Two distinct samples may have the same mean or median, but completely different levels of variability, or vice versa.

The standard deviation tells you how much, on average things vary from the mean of your population.

The range tells you the difference between the largest and smallest values.

Thus the standard deviation gives you an idea of how much every element of your population varies from the average whereas the range just tells you the maximum variation.