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jackiefrost
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If I have a sample consisting of n measurements why is the sample variance the result of dividing by n-1 instead of n?
jf
jf
jackiefrost said:If I have a sample consisting of n measurements why is the sample variance the result of dividing by n-1 instead of n?
jf
maverick280857 said:Well, if you have (n-1) then the expectation of the so defined sample variance exactly equals the population variance.
Tedjn said:I have had the same problem understanding this issue. Frequently, textbooks and online websites gloss over the issue with a pithy and unsatisfactory statement about degrees of freedom, leaving me to wonder whether the real explanation has anything to do with degrees of freedom at all.
Tedjn said:Why is this, or is division by n-1 just a better estimator than division by n in the finite case. If so, why?
Sample variance is a statistical measure of how spread out a set of data points are from the mean. It is important because it allows us to quantify the variability in our data and make comparisons between different groups or samples.
Dividing by n-1 instead of n is known as using Bessel's correction, and it is necessary when calculating sample variance because it provides an unbiased estimate of the population variance. Without it, the sample variance tends to underestimate the true population variance.
Sample variance is calculated using a subset of data points from a larger population, while population variance uses all data points from the entire population. Sample variance is an estimate of the population variance and is used when the entire population cannot be measured.
Sample variance should be used when the entire population cannot be measured, such as in scientific experiments or surveys. It is also useful when comparing different groups or samples within a population.
One limitation of sample variance is that it assumes the data is normally distributed. If the data is not normally distributed, it may not provide an accurate measure of variability. Additionally, sample variance is affected by outliers in the data, so it may not be the best measure of variability in these cases.