Journal of Statistics: Advances in Theory and ApplicationsAuthor's: Martin Bachmaier
Pages: [25] - [39]
Received Date: September 19, 2010
Submitted by:
The objective of this article is to address the frequently found academic opinion that in order to calculate the population variance, the sum of the squared deviations from the mean should be divided by the non-reduced number of summands, and not, as is the case for the sample variance, by one less. In reality, the question regarding the subtraction of one has nothing to do with whether it concerns a population or a sample; the decisive factor is whether the sum of squares refers to all measurement values or to characteristic values that are equally probable (or frequent). In the latter case, the full number is the divisor. However, if the sum of squares contains all measurement values of a sample or a population, one must be deducted from the overall number before it can be considered suitable as a divisor. Nevertheless, and precisely because of this subtraction, the variance becomes an average spread in the sense that it is not subject to a trend with regard to the number of data points, so that variances of populations of different sizes can be compared to each other. To better understand the latter part, an alternative variance definition is used, which instead of deviations from the mean refers to pairwise differences and in this respect characterizes the nature of variance more accurately. Therefore, it should be taught as the actual variance definition.
variance definition, population variance, sample variance, unbiased estimate, sampling techniques, semivariance.
