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Can the mean be less than the standard deviation?
In general, a mean can be greater or less than the standard deviation.
Is it possible that the standard deviation is less than one?
Yes, a standard deviation can be less than one.
Can standard deviation be greater than mean?
Standard deviation can be greater than the mean.
How do you know if a z score is positive or negative?
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.
What does it indicate if the mean is greater than the standard deviation?
It does not indicate anything if the mean is greater than the standard deviation.
Can a standard deviation be less than 1?
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!
Is the standard deviation best thought of as the distance from the mean?
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.
How do you calculate mean and Median smaller then Standard deviation?
In the same way that you calculate mean and median that are greater than the standard deviation!
Is standard deviation always smaller than mean?
No.
What does it mean if the standard deviation is less than the mean?
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.
Is the mean for a set of data always greater than the standard deviation?
Yes; the standard deviation is the square root of the mean, so it will always be larger.
How is standard deviation different from mean absolute decation?
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.
