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Earn +20 ptsQ: Can the mean be less than the standard deviation?
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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.
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.
Suppose z has a standard normal distribution with a mean of 0 and a standard deviation of 1. the probability that z is less than 1.15 is?
probability is 43.3%
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