eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2333-4576 2014-10-15 2 5 344 351 10.12691/ajams-2-5-8 AJAMS2014258 article Fumito Muguruma muguruma-fumito@mhlw.go.jp 1 Statistics and Information Department, Minister's Secretariat, Ministry of Health, Labour and Welfare, Kasumigaseki, Chiyoda-ku, Tokyo, JAPAN Considering a natural model of systematic sampling, we can calculate the expectation of statistic exactly as it is without regarding it as any other sampling methods. I will demonstrate the details of calculation and get some results. It can be shown that the sample mean of systematic sampling is an unbiased estimator of population mean. Variance of sample mean can be described explicitly and depends on how to sort a population list. Sum of the variance of sample mean and the mean of sample variance is kept constant between random and systematic sampling. As the sample size becomes larger, the variance of sample mean converges to 0. http://pubs.sciepub.com/ajams/2/5/8/ajams-2-5-8.pdf systematic sampling roulette model