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Can the Variance ever be smaller than standard deviation?
Yes. If the variance is less than 1, the standard deviation will be greater that the variance. For example, if the variance is 0.5, the standard deviation is sqrt(0.5) or 0.707.
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.
What is mean deviation and why is quartile deviation better than mean deviation?
What is mean deviation and why is quartile deviation better than mean deviation?
With a standard deviation of 0.01 inches and a mean of 0.55 inches what percentage of will be greater than 0.57?
Prob(X > 0.57) = Prob(Z > 2) = 0.02275 = 2.275%
What is considered a high standard deviation?
There's no valid answer to your question. The problem is a standard deviation can be close to zero, but there is no upper limit. So, I can make a statement that if my standard deviation is much smaller than my mean, this indicates a low standard deviation. This is somewhat subjective. But I can't make say that if my standard deviation is many times the mean value, that would be considered high. It depends on the problem at hand.
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 the mean be less than the standard deviation?
In general, a mean can be greater or less than the standard deviation.
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 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.
What are all the values a standard deviation can take?
The standard deviation must be greater than or equal to zero.
Why is the standard error a smaller numerical value compared to the standard deviation?
Let sigma = standard deviation. Standard error (of the sample mean) = sigma / square root of (n), where n is the sample size. Since you are dividing the standard deviation by a positive number greater than 1, the standard error is always smaller than the standard deviation.
What is the difference between a general normal curve and a standard normal curve?
A standard normal distribution has a mean of zero and a standard deviation of 1. A normal distribution can have any real number as a mean and the standard deviation must be greater than zero.
What is the z score of 1.0?
It is the value that is one standard deviation greater than the mean of a Normal (Gaussian) distribution.
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.
Can a standard deviation be greater than its mean?
Yes - but the distribution is not a normal distribution - this can happen with a distribution that has a very long tail.
How does one interpret a standard deviation which is more than the mean?
Standard deviation is a measure of the dispersion of the data. When the standard deviation is greater than the mean, a coefficient of variation is greater than one. See: http://en.wikipedia.org/wiki/Coefficient_of_variation If you assume the data is normally distributed, then the lower limit of the interval of the mean +/- one standard deviation (68% confidence interval) will be a negative value. If it is not realistic to have negative values, then the assumption of a normal distribution may be in error and you should consider other distributions. Common distributions with no negative values are gamma, log normal and exponential.
Can the Variance ever be smaller than standard deviation?
Yes. If the variance is less than 1, the standard deviation will be greater that the variance. For example, if the variance is 0.5, the standard deviation is sqrt(0.5) or 0.707.
