I know that $\left<x\right>$ is 80. But when it is written that $\Delta x/\left<x\right> = 0.2$, I don't know immediately how to do a sampling of $x$, since standard deviation is mostly written in $\sigma$ but not $\Delta$.

Does this mean that the distribution of $x$ is a normal distribution? Also does it imply the standard deviation being 16 or the variance being 16?

(The only word description is that the distribution of $x$ is sufficiently peaked at 80)

  • $\begingroup$ Why only those two rather than say mean deviation? I've seen $\Delta$ used for that before. $\endgroup$
    – Glen_b
    Jul 12, 2017 at 6:45
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    $\begingroup$ (1) Where have you seen those symbols? Please provide some reference since neither of those is commonly used. The symbols should be defined in your source. (2) $\Delta$ is commonly used to denote "change", I haven't seen it used for SD or variance. (3) The fact that you can compute mean and sd for some variable does not imply anything about it's distribution... $\endgroup$
    – Tim
    Jul 12, 2017 at 7:33
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    $\begingroup$ Also, full width at half maximum mathworld.wolfram.com/FullWidthatHalfMaximum.html is another way to summarize spread. $\endgroup$
    – Nick Cox
    Jul 12, 2017 at 8:49
  • $\begingroup$ it does use to denote standard deviation in physics web.mit.edu/~emin/www.old/writings/quantum/img37.gif , but this is not sampling though (although i am reading a physics article) $\endgroup$
    – Ka Wa Yip
    Jul 12, 2017 at 9:17
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    $\begingroup$ @kyle Not in general. This thread can at best be speculative unless and until you show a source we can understand to explain. $\endgroup$
    – Nick Cox
    Jul 12, 2017 at 10:00

1 Answer 1


Δ is usually used to denote a change. Is it possible that this denotes a percentage of change of x compared to either the new or the old x? Can you edit your question to give more information about the specific situation?

  • $\begingroup$ I think this is a good guess but from the formula given the quantity might be fractional change, but not percent. $\endgroup$
    – Nick Cox
    Jul 12, 2017 at 8:28
  • $\begingroup$ Yes, you are of course totally right, my mistake! Wrong word choice $\endgroup$
    – Tami
    Jul 12, 2017 at 8:46
  • $\begingroup$ i found that it may mean indeed follow a normal distribution. if it is normal distribution, and the $\Delta$ means change, does it mean that standard deviation or variance? This should also be always positive. $\endgroup$
    – Ka Wa Yip
    Jul 12, 2017 at 9:27

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