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I am having a below case where N = 300 , Mean = 67 and SD = 30. With the above data we can say the variance is high because of SD = 30. My question is how we are defining it as high on what basis we are evaluating the SD is high or low.

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    $\begingroup$ "With the above data we can say the variance is high because of SD = 30. My question is how we are defining it as high on what basis we are evaluating the SD is high or low." You're the only person that can answer that question. I have no way of divining why you are saying variance is high because the standard deviation is 30! $\endgroup$ – Sycorax Feb 8 '16 at 13:05
  • $\begingroup$ I voted to keep this open because I see the question all of the time and it does have straightforward answers that, while not directly solving this problem tell how to solve it. $\endgroup$ – John Feb 8 '16 at 13:10
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    $\begingroup$ Possible duplicate of What does the size of the standard deviation mean? $\endgroup$ – Tim Feb 8 '16 at 13:19
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The way you determine qualitative or relative statements like high or low variance of a sample has to do with knowing something about the kind of data you're dealing with. If you had a computer simulation and it tended to run with variances of tiny fractions of a second and all of a sudden they started coming in with multi-second variances then you'd call that high and wonder what was happening. If you were studying human reaction times and they typically had SDs of about 80 within a person and you found a subject who consistently had an SD of about 20 then that would be pretty low and you might inquire if they were a drag racer.

In short, the way you make such statements is to understand your subject matter. Reasonable qualitative statements are good to make when reporting your results because it reflects that knowledge. It is often very useful in determining both the authors experience and the context those numbers should be placed in for initiates.

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