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I have derived the following response time data for a performance test I am running:

Min - 8sec Max - 284sec Average - 28sec Standard Deviation - 27sec

What does the standard deviation say about the response time data distribution? When you say low/high standard deviation, what does this actually mean? Is this in comparison to the Average/Min/Max?

I know what standard deviation is and how it's computed. I'm just not sure how to tell if it is high or low.

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  • $\begingroup$ "I know what standard deviation is". Hmm ... if you do know what standard deviation is, you should know that it is a measure of dispersion of data ... $\endgroup$
    – user1551
    Commented Dec 17, 2012 at 10:38
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    $\begingroup$ Yes, what confuses me is how to tell if a standard deviation is high or low. The examples I've read so far have not said what makes it high or low. $\endgroup$
    – rro
    Commented Dec 17, 2012 at 10:53
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    $\begingroup$ Aren't terms like "high" or "low" just a matter of subjective judgement? The data you have seem to suggest that time is very roughly speaking 28sec +/- 27 sec, so in a very naive sense you expect the results to usually fall between 1sec and 60sec. I'd say it's rather high deviation, but I suppose it depends on the characteristic of a problem. $\endgroup$
    – Jakub Konieczny
    Commented Dec 17, 2012 at 11:00

2 Answers 2

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If you take your cues from the financial industry, you can use the coefficient of variation (CV), which is the standard deviation / mean. This formula is used to normalize the standard deviation so that it can be compared across various mean scales.

As a rule of thumb, a CV >= 1 indicates a relatively high variation, while a CV < 1 can be considered low.

Some references to usage as "rule of thumb"

http://www.readyratios.com/reference/analysis/coefficient_of_variation.html

http://www.mhnocc.org/forum/index.php?t=msg&goto=234&

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  • $\begingroup$ Could you please share your source of information for this? $\endgroup$
    – rro
    Commented Dec 20, 2012 at 1:59
  • $\begingroup$ I have listed a couple of references above. $\endgroup$
    – Ralph Winters
    Commented Dec 20, 2012 at 17:00
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    $\begingroup$ It seems dubious to me to extend this outside of the financial industry (if that's where its used). Logically the CV can only be greater than 1 if the Std deviation is higher than the mean. Which in most data sets seems unlikely. $\endgroup$
    – Morvael
    Commented Nov 9, 2020 at 11:36
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    $\begingroup$ @Morvael the CV was invented by Karl Pearson more than a century ago, who is deemed as the founder of mathematical statistics. The fact that is used by the financial industry is a sign of how widely is used, not of a lack of "mathematical seriousness" if you will. $\endgroup$
    – Arturo Ortiz Tapia
    Commented Dec 20, 2023 at 3:08
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When trying to figure this out myself I opted for using the Std deviation as a percentage of the range. Looking at this graph:

enter image description here

from that image I would I would say that the SD of 5 was clustered, and the SD of 20 was definitionally not, the SD of 10 is borderline.

More mathematically,

  • The SD of 5 has 68% of the values within 10% of the range
  • The SD of 10 has 68% of the values within 20% of the range
  • The SD of 20 has 68% of the values within 40% of the range

So as a purely internal measure of High / Low Std deviation I chose to say if the SD was less than 10% of the range then its low, greater than 10% of the range then high.

But you could of course choose different percentages based on your own data sets.

https://www.scribbr.com/statistics/standard-deviation/

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