# range vs. standard deviation

Six Sigma – iSixSigma Forums Old Forums General range vs. standard deviation

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• #28869

mat
Participant

I am new to the spc game and I am curious what the difference is between range and standard deviation?

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#72579

Kevin Hankins
Participant

1. Go to http://www.aecouncil.com/data_analysis to get DE Histograms (free).
2. Click on “Give me some data in Excel”.
3.  Select some cells, and then click on “Normal Random Numbers Fill”.
4.  Find the range of your Sample from Step 3 (you can use Max()-Min()).
5.  Find the stdev() of the same Sample.
6.  Repeat.
7.  You will find that Rbar ~= stdev*d2.
d2(n) is listed in many statistics texts Appendices.

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#72597

Savage
Participant

The range is a measure of variation. The range is used in computing the “estimated standard deviation” = R-bar/d2. The other standard deviation, “sigma of the individual values” or “sample standard deviation” does not use the range of the data to calculate the standard deviation.
I.e. The weather report tonight will likely say that today’s high was X and low was Y. The difference is the range and it shows you how much variation there was in temperature. The same report could say that the average temperature today was Z and the standard deviation was X.

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#72619

Peter Wooding
Participant

Range is a fact – the difference between largest and smallest values for a group of samples taken from a larger population (or, sometimes, the difference between consecutive samples).
Standard Deviation (for the samples) is also a fact (the ‘root mean square’ of deviations from the average value) but it’s really all about probability: a measure of the ‘likely’ deviation from the average. As other contributors have said, there is a shortcut for calculating it from successive range figures (as an alternative to the ‘rms’ method) but, whichever way it’s calculated, there’s an implicit assumption that the probability of a small deviation is greater than the probability of a large deviation. This is typically referred to as a NORMAL distribution, for which almost 100% (actually 99.7%) of samples would be expected to have a deviation of less than 3 x Std Dev. In other words, if you took 1000 samples you might expect to get 3 with a larger deviation than this (you might actually get more, or you might not get any!). Approx 68% would be expected to have a deviation less than the Std Dev.

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#72621

Jim deVries
Participant

mat,
all the previous answers are theortically correct.
From a practical viewpoint, an another question could be discussed on whether the range or standard deviation is best suited in applications.
If your process is normal; std deviation.  However, if your data is not normal; range, span, stability factor and median will be better describe the process.
The biggest danger in applying standard SPC charts is when the data is not normal is never going to be normal (most transactional processes).
Warning: one of the most creative mistakes in applying SPC is to take the average of data to make it normal.  If you do this, you are hiding the defects and it will take longer to find when you have an out-of-control event.
I hope that this helps.
CHeers!

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