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The standard deviation of a set of data is a measure of the random variability present in the data. Given any two sets of data it is extremely unlikely that their means will be exactly the same. The standard deviation is used to determine whether the difference between the means of the two data sets is something that could happen purely by chance (ie is reasonable) or not.

Also, if you wish to take samples of a population, then the inherent variability - as measured by the standard deviation - is a useful measure to help determine the optimum sample size.

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Q: What is the purpose of finding standard deviation?

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1. establishment of standard 2. fixation of the standard 3. compairing actual performance with standard performance 4. finding out the deviation 5. correcting the deviation

Usually a normal distribution.

The standard deviation is the standard deviation! Its calculation requires no assumption.

The standard deviation of the population. the standard deviation of the population.

The standard deviation is 0.

I am not entirely sure I understand correctly what you mean by "essence". However, the idea of finding the standard deviation is to determine, as a general tendency, whether most data points are close to the average, or whether there is a large spread in the data. The standard deviation means, more or less, "How far is the typical data point from the average?"

The purpose is to show how close one answer is to the other. Basically, to show how far off an answer is.

Information is not sufficient to find mean deviation and standard deviation.

The standard deviation in a standard normal distribution is 1.

Standard error of the mean (SEM) and standard deviation of the mean is the same thing. However, standard deviation is not the same as the SEM. To obtain SEM from the standard deviation, divide the standard deviation by the square root of the sample size.

Yes

Standard deviation is a measure of the spread of data.

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