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I learn some statistics some times ago. It has been while but I still remember some characteristics and property of the normal distribution. One of them is the standard deviation could be used to estimated the probability of finding the entity around the mean in the range ##[-n\sigma, +n\sigma]## with ##n=1, 2, 3## is estimated to be 68%, 95% and 99.7%, so for normal distribution, standard deviation is used to estimated the dispersion of the data. But today, I got some data from somewhere. I plot it in matlab, the distribution is not symmetric, one side has very steep edge and the other end is a long tail. From what I am understanding that standard deviation(SD) is just an algorithm so it is not a feature of normal distribution only.

So can I say the SD for arbitrary distribution has the significance of estimating the dispersion of the data?

For non-symmetric distribution with one side is a long tail. What is the significance of SD? In the data I have, the mean value is about x=40 (a sharp peak appear at 55 when plot it as histogram), the SD is about 52 but the left side to the mean drop to zero when x=29 and gradually decrease to zero on the right side at x = 300. One thing I know is the x must be positive number. So I can't say the probability of finding the data in the range [40-52=-12, 40+52=92] is 68%. It is confusing me

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# I About standard deviation

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