ExplanationThe average of your data summarises it all in a single value. That certainly throws away a lot of information. If you were to know one more thing about the data, after the average, what would be the most useful thing? The range (largest and smallest) might be useful, but there is a different measure that is even better - the standard deviation.
The standard deviation measures how much the data varies:
- A large number means the data varies a lot
- A small number means the data varies a little
- A standard deviation of zero indicates that all the values in the data are identical
For example, the standard deviation of temperature in Florida is less than it is in New York.
The standard deviation tells you something more about the average too, as it measures variation in terms of how far from the mean all the values in the sample fall. Values are further from the mean on average when standard deviation is large than they are when it is small.
The symbol for the standard deviation is of a sample of data is s.