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Fundamentals of Statistics 1: Basic Concepts :: Describing the Variability of Data
The center of a distribution of data is helpful in telling you something about the most common values, but it doesn't tell you much about how spread out or variable the values are. To describe variability, we need an additional measure.
Range
An intuitive first start would be to provide the minimum and maximum values. The difference between the min and max values is called the
range
, and this is one of the simplest ways to describe the variability.
The problem with the range is that it by definition looks at the most extreme values in your data. What we want is some way of describing the
average or typical distance each value is from the mean
.
Standard Deviation
The most common measure of the average distance is the standard deviation. The formula for the standard deviation is below.
It looks more confusing that what is actually happening. To
get a measure of standard deviation
you just:
subtract each value from the mean
square the difference score
add up all those squared differences scores
divide by the sample size.
take the square root.
Variance
A closely related measure to the standard deviation is the
variance
. The formula for the variance is below.
You'll notice they are very similar. In fact, the only difference between the two is that in the variance you don't take the square root of the sum of the difference scores. The variance is often used in many statistical formula, but since the values are describing the average squareddistance to the mean, its hard to understand. To make it a more intuitive measure, we take the square root so we have the typical distance each value is from the mean.
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July 27, 2012  Zapurzza wrote:
i guess an example then calculation and meaning what would these numbers mean can help
January 25, 2012  Jeff Sauro wrote:
Suresh, Thanks for finding that, I fixed the order now.
January 24, 2012  Suresh Batta wrote:
Steps 4 & 5 for standard deviation are reversed.
July 29, 2011  JeffACT wrote:
I think the formulas could be better explained with notations on the variables.
May 16, 2010  Jim Franck wrote:
It might be helpful to add a sentence or two describing what the idea behind having a "variance" is. Seems many of the texts I've read describe how to calculate it but fail to give any reason to do so. What good is knowing the variance anyway? Curious minds... and all that. By the way, your tutoria!s are terrific! You simplify concepts and make them very understandable. A real feat in this realm!