Standard deviation (SD) is neither biased nor unbiased. Estimates for SD can be biased but that depends on the formula used to calculate the estimate.
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Biased- (Not random) Unbiased-(Random) Example: (ubbiased) Woman takes random people to take a survey.
The standard deviation is the standard deviation! Its calculation requires no assumption.
A biased error is one that is caused by a factor inherent to the source of the error. An unbiased error is one that comes from anywhere.
The standard deviation. There are many, and it's easy to construct one. The mean of a sample from a normal population is an unbiased estimator of the population mean. Let me call the sample mean xbar. If the sample size is n then n * xbar / ( n + 1 ) is a biased estimator of the mean with the property that its bias becomes smaller as the sample size rises.
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.