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Yes, the mean deviation is typically less than or equal to the standard deviation for a given dataset. The mean deviation measures the average absolute deviations from the mean, while the standard deviation takes into account the squared deviations, which can amplify the effect of outliers. Consequently, the standard deviation is usually greater than or equal to the mean deviation, but they can be equal in certain cases, such as when all data points are identical.
What else can I help you with?
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.
If data set A has a larger standard deviation than data set B data set A is less spread out than data set B.?
This statement is incorrect. If data set A has a larger standard deviation than data set B, it indicates that data set A is more spread out, not less. A larger standard deviation reflects greater variability and dispersion of data points from the mean, while a smaller standard deviation suggests that data points are closer to the mean and thus less spread out.
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!
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 standard deviation always smaller than mean?
No.
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.
