SAMPLE VARIANCE AND FIRST-ORDER DIFFERENCES OF OBSERVATIONS

Abstract

It is proved that the variance of a sample can be calculated from first-order differences of its observations. It can also be represented by a quadratic form in the differences of the observations via a constant matrix (depending on the sample size) which is open for further study. Avoiding use of the mean in the calculation of the variance is expected to increase precision, especially if computer programs are used. An alternative method is also presented for the calculation of the variance from a frequency distribution.