No, the standard deviation is a measure of the entire population.
The sample standard deviation is an unbiased estimator of the population. It is different in notation and is written as 's' as opposed to the greek letter sigma.
Mathematically the difference is a factor of
n/(n-1)
in the variance of the sample. As you can see the value is greater than 1 so it will increase the value you get for your sample mean.
Essentially, this covers for the fact that you are unlikely to obtain the full population variation when you sample.
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The standard deviation is the square root of the variance.
A single observation cannot have a sample standard deviation.
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.
If the population standard deviation is sigma, then the estimate for the sample standard error for a sample of size n, is s = sigma*sqrt[n/(n-1)]
Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size.