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What is the difference between a biased and unbiased sample?
Biased- (Not random) Unbiased-(Random) Example: (ubbiased) Woman takes random people to take a survey.
What are the assumptions of standard deviation?
The standard deviation is the standard deviation! Its calculation requires no assumption.
Difference between biased and unbiased errors?
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.
What biased estimator will have a reduced bias based on an increased sample size?
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.
Is sample standard deviation the same as standard deviation?
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.
