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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?"
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What is standard deviation used for?
Standard deviation is a measure of the spread of data.
If the standard deviation is small the data is more dispersed?
No, if the standard deviation is small the data is less dispersed.
Relation between mean and standard deviation?
Standard deviation is the variance from the mean of the data.
What does a standard deviation of 0 tell you?
The smaller the standard deviation, the closer together the data is. A standard deviation of 0 tells you that every number is the same.
How do you identify group data or ungroup data in standard deviation?
You cannot. If you are told the standard deviation of a variable there is no way to tell whether that was derived from grouped or ungrouped data.
