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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:
The standard deviation is the typical or average distance a value is to the mean
If all values are the same, then the standard deviation is 0
The standard deviation is heavily influenced by outliers just like the mean (it uses the mean in its calculation).
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.
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November 25, 2018  Sagar wrote:
7077250712
October 14, 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 3, 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 27, 2012  Loriemae wrote:
The coefficient variance
June 18, 2012  Daudi wrote:
Nothing
February 18, 2012  Guillermo ermel wrote:
Could the cv be higher than 100%? What would that mean?