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Describing the Center of Data
Home What is Statistics? A Population and Sample A Parameter and a Statistic Quantitative and Categorical Data Discrete and Continuous Nominal, Ordinal, Interval and Ratio Describing the Center of Data Describing the Variability of Data The Standard Deviation and Coefficient of Variation The Empirical Rule Percentiles and The Five-Number SummaryView All Tutorials
 The Standard Deviation and Coefficient of Variation
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:
  1. subtract each value from the mean
  2. square the difference score
  3. add up all those squared differences scores
  4. divide by the sample size.
  5. 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 squared-distance 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.


 
Describing the Center of Data
Home What is Statistics? A Population and Sample A Parameter and a Statistic Quantitative and Categorical Data Discrete and Continuous Nominal, Ordinal, Interval and Ratio Describing the Center of Data Describing the Variability of Data The Standard Deviation and Coefficient of Variation The Empirical Rule Percentiles and The Five-Number SummaryView All Tutorials
 The Standard Deviation and Coefficient of Variation

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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 | Jeff-ACT 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!