Variance and Standard Deviation
Deviations about the mean of a population is the basis for most of the statistical tests we will learn. Since we are measuring how widely a set of scores is dispersed about the mean we are measuring variability. We can calculate the deviations about the mean, and express it as variance or standard deviation. It is very important to have a firm grasp of this concept because it will be a central concept throughout the course.
Both variance and standard deviation measures variability within a distribution. Standard deviation is a number that indicates how much, on average, each of the values in the distribution deviates from the mean (or centre) of the distribution. Keep in mind that variance measures the same thing as standard deviation (dispersion of scores in a distribution). Variance, however, is the average squared deviations about the mean. Thus, variance is the square of the standard deviation.
In terms of quality of goods/services, It is important to know that higher variation means lower quality. Measuring the size of variation and its source is the statistician's job, while fixing it is the job of the engineer or the manager. Quality products and services have low variation.