Population Variance Vs Sample Variance Math

When dealing with the complete population the population variance is a constant a parameter which helps to describe the population.

Population variance vs sample variance math. Variance is calculated in five steps. Estimating the population variance by taking the sample s variance is close to optimal in general but can be improved in two ways. The main difference between population variance and sample variance relates to calculation of variance. First mean is calculated then we calculate deviations from the mean and thirdly the deviations are squared fourthly the squared deviations are summed up and finally this sum is divided by number of items for which the variance is being calculated.

So far it was the same for both population and sample variance. In our example 2 i divide by 99 100 less 1. Population is the whole group. Most simply the sample variance is computed as an average of squared deviations about the sample mean by dividing by n.

Difference between population variance and sample variance as seen a distinction is made between the variance σ 2 of a whole population and the variance s 2 of a sample extracted from the population. A sample is a part of a population that is used to describe the characteristics e g. The size of a sample can be less than 1 or 10 or 60 of the population but it is never the whole population. Before we dive into standard deviation and variance it s important for us to talk about populations and population samples.

When i calculate sample variance i divide it by the number of items in the sample less one. Mean or standard deviation of the whole population. When i calculate population variance i then divide the sum of squared deviations from the mean by the number of items in the population in example 1 i was dividing by 12.