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Describing the Variability 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 Empirical Rule
Fundamentals of Statistics 1: Basic Concepts :: The Standard Deviation and Coefficient of Variation

Properties of the Standard Deviation

In terms of measuring the variability of spread of data, we've seen that the standard deviation is the preferred and most used measure.


Some additional things to think about the standard deviation:
  1. The standard deviation is the typical or average distance a value is to the mean
  2. If all values are the same, then the standard deviation is 0
  3. The standard deviation is heavily influenced by outliers just like the mean (it uses the mean in its calculation).
  4. The sample standard deviation is denoted with the letter s and the population standard deviation is denoted with the lower case Greek letter sigma σ.
If your data is more spread out (has more variability) then you will have a higher standard deviation. It's often difficult to interpret a standard deviation since it's based on the sample of data. Is a standard deviation of 12 high or is a .20 high? 

Coefficient of Variation (CV)

If you know nothing about the data other than the mean, one way to interpret the relative magnitude of the standard deviation is to divide it by the mean. This is called the coefficient of variation. For example, if the mean is 80 and standard deviation is 12, the cv = 12/80 = .15 or 15%.

If the standard deviation is .20 and the mean is .50, then the cv = .20/.50 = .4 or 40%. So knowing nothing else about the data, the CV helps us see that even a lower standard deviation doesn't mean less variable data.

I've found the CV to be an underused metric considering it is so simple to compute and helps a lot with understanding relative variability.

 
Describing the Variability 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 Empirical Rule

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November 26, 2018 | Sagar wrote:
7077250712
 
October 15, 2018 | Celestine Espares wrote:
n./a
 
May 11, 2017 | jaf wrote:
Sample vs. population? If you have 19 items, is the population 19? If you measure only 3, are they the sample then? Are there different equations? How would you know whether or not 3 would be a good sample size for 19? Etc..
 
March 22, 2015 | Alois Pukienei wrote:
Was very clear
 
February 4, 2015 | miabricknell wrote:
I'm in grade 8, none of this made sense!
 
February 3, 2015 | moakhir wrote:
really nice and self explinatory
 
June 4, 2014 | rr wrote:
practical examples of CV usage
 
January 21, 2013 | Prafulla Chandra Tiwari wrote:
u have not given the formula of sd n cv which i was searching
 
November 28, 2012 | Loriemae wrote:
The coefficient variance
 
June 19, 2012 | Daudi wrote:
Nothing
 
February 18, 2012 | Guillermo ermel wrote:
Could the cv be higher than 100%? What would that mean?