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Q: Can the mean be less than the standard deviation?

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No. A small standard deviation with a large mean will yield points further from the mean than a large standard deviation of a small mean. Standard deviation is best thought of as spread or dispersion.

No.

Yes; the standard deviation is the square root of the mean, so it will always be larger.

If the mean is less than or equal to zero, it means there has been a serious calculation error. If the mean is greater than zero and the distribution is Gaussian (standard normal), it means that there is an 84.1% chance that the value of a randomly variable will be positive.

probability is 43.3%

Related questions

Yes, a standard deviation can be less than one.

Standard deviation can be greater than the mean.

It does not indicate anything if the mean is greater than the standard deviation.

A negative Z-Score corresponds to a negative standard deviation, i.e. an observation that is less than the mean, when the standard deviation is normalized so that the standard deviation is zero when the mean is zero.

No. A small standard deviation with a large mean will yield points further from the mean than a large standard deviation of a small mean. Standard deviation is best thought of as spread or dispersion.

Yes. Standard deviation depends entirely upon the distribution; it is a measure of how spread out it is (ie how far from the mean "on average" the data is): the larger it is the more spread out it is, the smaller the less spread out. If every data point was the mean, the standard deviation would be zero!

No.

In the same way that you calculate mean and median that are greater than the standard deviation!

Yes; the standard deviation is the square root of the mean, so it will always be larger.

If the mean is less than or equal to zero, it means there has been a serious calculation error. If the mean is greater than zero and the distribution is Gaussian (standard normal), it means that there is an 84.1% chance that the value of a randomly variable will be positive.

If I have understood the question correctly, despite your challenging spelling, the standard deviation is the square root of the average of the squared deviations while the mean absolute deviation is the average of the deviation. One consequence of this difference is that a large deviation affects the standard deviation more than it affects the mean absolute deviation.

Standard deviation in statistics refers to how much deviation there is from the average or mean value. Sample deviation refers to the data that was collected from a smaller pool than the population.

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