Question

When do we use the mean and standard deviation to describe a distribution?

Answer 1

Mean refers to the arithmetic mean in most of the cases, but is also ambiguous. And standard deviation is the average distance of each score from the mean . Sometimes it is useful to calculate how far, in standard deviations, a data element was from the mean.

We use mean and standard deviation to describe the normal distribution. In this distribution , to calculate the probabilities, we calculate a new parameter called z score using mean and standard deviation for each data element. It is also termed as standard score. Since many data sets have a somewhat normal distribution, it is a very helpful way to compare data elements from different populations which may very well have differing means and standard deviations.