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Is the normal distribution always being defined by the mean and standard deviation?
Yes, the normal distribution is uniquely defined by its mean and standard deviation. The mean determines the center of the distribution, while the standard deviation indicates the spread or dispersion of the data. Together, these two parameters specify the shape and location of the normal distribution curve.
What else can I help you with?
In the standard normal distribution the standard deviation is always what?
The standard deviation in a standard normal distribution is 1.
Why the standard deviation of a set of data will always be greater than or equal to 0?
Because it is defined as the principal square root of the variance.
Why use standard deviation and not average deviation?
Because the average deviation will always be zero.
How do you calculate standard deviation without a normal distribution?
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.
What is the definition of Standard deviation of a single measurement?
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!
In the standard normal distribution the standard deviation is always what?
The standard deviation in a standard normal distribution is 1.
How do you derive mean deviation from mean for pareto distribution?
The total deviation from the mean for ANY distribution is always zero.
Why the standard deviation of a set of data will always be greater than or equal to 0?
Because it is defined as the principal square root of the variance.
Why use standard deviation and not average deviation?
Because the average deviation will always be zero.
How do you calculate standard deviation without a normal distribution?
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.
Will the standard error always be lower than the standard deviation?
No.
Does standard deviation and mean deviation measure dispersion the same?
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.
What is the definition of Standard deviation of a single measurement?
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!
What is the standard deviation of the data set given below?
A single number, such as 478912, always has a standard deviation of 0.
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 is he standard deviation of the data set given below 478912?
A single number, such as 478912, always has a standard deviation of 0.
Is standard deviation always smaller than mean?
No.
