Section 3.2

Fundamentals of Social Statistics

 

Measures of Variability

Variability is also referred to as dispersion or spread.  These terms all refer to differences among scores.  These differences indicate how subjects vary.  Measures of dispersion (a synonym of variability) identify how “spread out” a data set is, relative to the center. This provides a way of determining if the members of a data set tend to be very close to each other or if they tend to be widely scattered. In other words, how much does each subject’s score differ from the average?  In most research reports, you will find a measure of variability reported along with a measure of central tendency.  These two statistics, along with a discussion of shape, adequately describe a distribution of scores.  The amount of variation in a group of scores is important for both statistical and practical reasons.  Simply put, a measure of center often does not tell the whole story.

For example, according to the Bureau of the Census, the median household income for the United States is $50,233.00.  That makes it sound like most Americans are all doing pretty well.  If we just look that the median (a measure of center), we miss the fact that poverty is still a big problem in the United States.  We would not know that about 15% of Americans live in poverty.  We would not know that around 27% of single-parent families live in poverty.  We would not know that a much larger proportion of minorities live in poverty than whites.  These problems with observing only a measure of center arise because individuals tend to vary widely from the center.  To get an idea of the larger picture, we have to look at the center, but we must also consider variability.

The more variable a group's scores, the more heterogeneous the group is.  Conversely, the smaller the variation, the more homogenous the group is.

 


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Last Modified:  02/18/2019

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