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Is it possible for the standard deviation to be greater than the mean?

Is it possible for the standard deviation to be greater than the mean?

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Is it possible for the standard deviation to be greater than the mean? If so, is there any example case that this could happen? What would be the best approach to handle this?

1 Answer

365 Team
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Hey Melissa,

There is no issue for the standard deviation to be greater than the mean. Simply take the Standard Normal distribution, which has a mean of 0 and a standard deviation of 1.
To get a standard deviation greater than the mean it means that the data allows for negative values. Hence, if you’re working with quantities of something (or even money) this issue won’t happen. If variable that matches this description does allow for negative values, then there’s nothing to worry about.

Best,
365 Vik

Hi Vik, thanks for the answer! So if the data does not allow for negative values, then it will be a problem. Could it be because of bad data? And could log transformation helps?

4 months

Hi Melissa, I think it’s not mathematically possible for this to happen unless there are negative values in the data. Hence, it would be a problem if it happened. It could be due to bad data, since missing/inaccurate values change the mean and standard deviation of the data set. You could try a log transformation, but I don’t think it help in this scenario.

3 months