In this lecture we will talk about range, variance, standard deviation, and coefficient of variation for ungrouped or raw data. The range is the difference between the largest observation of a data set and the smallest observation. The major disadvantage of the range is that it does not include all of the observations. Only the two most extreme values are included and these two numbers may be untypical observations. An important measure of variability is variance .
Variance is the average of the squared deviations from the arithmetic mean.
Find the arithmetic mean. Find the difference between each observation and the mean. Square these differences. Sum the squared differences. As you see in the above example, the variance is not expressed in the same units as the observations.