When describing the normal distribution as an underlying distribution of events in a sample, the researcher is really describing the probability of any given number or event to take place within the distribution itself. At first, one can become mired in the fact that distributions have to be generated for any given data set on a particular research topic, but once realizing that the relative frequency in a distribution of n is in fact “its probability” (Hinkle, Wiersma, & Jurs, 2003, p. 160). Therefore, one can begin to make inferences from the data that yield insights into future performance or behavior in a similar sample, depending on the research performed.
For any practitioner, it is important to realize this fact when conducting basic research so as to maximize the understanding of data collected. Among educational staff, in a K-12 district for example, being able to better understand what is actually analyzed, how, and what it all means is crucial to creating interventions or program enhancements that actually work. Using inferential statistics, and sampling correctly, can lead to strong data correlations, and therefore, yield more effective outcomes for the sample researched in the first place.
Many examples of introductory statistics seem to include descriptions of drawing slips of paper. (Hinkle et al., 2003) What is powerful, as an insight drawn from this exercise, is when the researcher realizes that the act of drawing pieces of paper is actually the inferences being made (in a future setting, where data is used for prediction) is very powerful.
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Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003). Applied Statistics for the Behavioral Sciences. 5th Ed. Boston: Houghton Mifflin.