Understanding the concepts of quantum mechanics has always been a challenge for undergraduate students. This is especially so because many of the introductory (analytically solvable) systems and problems discussed in textbooks are seemingly abstract. Using approximate experimental demonstrations of such systems and problems have been shown to be very helpful in teaching and illustrating the basic concepts of quantum mechanics. One such system is the particle-inside-a-ring system, whose experimental demonstration was achieved 25 years ago in the form of a "quantum corral" of iron atoms arranged in a ring on a copper surface by using scanning tunneling microscopy. However, this system, which can be a very good model to demonstrate the concepts of quantum mechanics, has not been treated in depth in the literature or in quantum-chemistry textbooks from an educational point of view. Here, we examine the particle-inside-a-ring system and its experimental demonstration in order to elucidate the difference between the superposition and statistical-mixture concepts and to provide an explicit description of how experimental data can be related (fitted) to a theoretical model.