Early studies on the development of theory of systematic sampling was as reported by Murthy (1967, p.134)
[2] while Cochran (1977) [1] reported that Madow (1953) [4] had carried systematic sampling to its logical conclusion
with his recommendation that a systematic sample be chosen at or near the center of the interval, i.e. instead
of starting the sequence by a random number chosen between 1 and k, we take the starting number as
(k +1 2 ) if k is odd and either k 2 or (k +1 2 ) if k is even