Calculating any statistical measures is easy if you have the population data. But in real cases, we work with the sample data which is the subset of population data. It means we have to make predictions about the population data using the sample data. It is likely to get inaccurate results as your sample may be biased or you may have a very small sample size.
This problem can be resolved by a little tweak in various statistical formulas when using sample data instead of population data. n-1 is used instead of n in the calculation of sample variance, sample standard deviation etc.
Let’s understand it by the standard deviation formula:
Standard Deviation is the measure of the dispersion of data. It is calculated by taking the root of variance. Below is the standard deviation formula for population and sample data.
Standard Deviation Formula
Let N be the population size and n be the sample size.
Population Standard Deviation
Sample Standard Deviation
What is Bessel’s Correction?
Bessel correction is the n-1 found in the sample formulas like sample variance and sample standard deviation.
Why do we use N-1 instead of N?
The sample contains a little bias in the data. Subtracting 1 from the sample size corrects the bias. Using n-1 in the sample formula helps to get an accurate prediction of the population data using the sample data.
Why is Bessel’s Correction used?
Bessel’s correction is used while working with the sample data.
As already discussed, it is an unbiased estimator of the population. It helps to achieve more accurate results using sample data.