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The standard deviation in a standard normal distribution is 1.
You calculate standard deviation the same way as always. You find the mean, and then you sum the squares of the deviations of the samples from the means, divide by N-1, and then take the square root. This has nothing to do with whether you have a normal distribution or not. This is how you calculate sample standard deviation, where the mean is determined along with the standard deviation, and the N-1 factor represents the loss of a degree of freedom in doing so. If you knew the mean a priori, you could calculate standard deviation of the sample, and only use N, instead of N-1.
Because it is defined as the principal square root of the variance.
Because the average deviation will always be zero.
The standard deviation of a single observation is not defined. With a single observation, the mean of the observation(s) would be the same as the value of the observation itself. By definition, therefore, the deviation (difference between observation and mean) would always be zero. Rather a pointless exercise!
The standard deviation in a standard normal distribution is 1.
The total deviation from the mean for ANY distribution is always zero.
You calculate standard deviation the same way as always. You find the mean, and then you sum the squares of the deviations of the samples from the means, divide by N-1, and then take the square root. This has nothing to do with whether you have a normal distribution or not. This is how you calculate sample standard deviation, where the mean is determined along with the standard deviation, and the N-1 factor represents the loss of a degree of freedom in doing so. If you knew the mean a priori, you could calculate standard deviation of the sample, and only use N, instead of N-1.
Because it is defined as the principal square root of the variance.
Because the average deviation will always be zero.
No.
No. The average of the deviations, or mean deviation, will always be zero. The standard deviation is the average squared deviation which is usually non-zero.
The standard deviation of a single observation is not defined. With a single observation, the mean of the observation(s) would be the same as the value of the observation itself. By definition, therefore, the deviation (difference between observation and mean) would always be zero. Rather a pointless exercise!
A single number, such as 478912, always has a standard deviation of 0.
Yes; the standard deviation is the square root of the mean, so it will always be larger.
A single number, such as 478912, always has a standard deviation of 0.
The following are the two main reasons.The first is that the inference to be made is usually (but not always) about the mean or standard deviation.Many probability distribution functions (but not all) can be defined in terms of these measures so identifying them is sufficient.They are well studied and their distributions are well known, along with tests for significance.