Final answer:
The concept discussed in the student's question is the Law of Large Numbers, which explains that larger sample sizes result in the experimental probabilities becoming closer to the theoretical probabilities, unlike small samples that are prone to greater variability.
Step-by-step explanation:
The concept described by the statement 'Although after many trials proportions do tend to even out, this does not extend to small samples' refers to the Law of Large Numbers. This law states that as the number of trials in a probability experiment increases, the difference between the theoretical probability of an event and the relative frequency probability approaches zero. In other words, the more trials are conducted, the experimental outcomes begin to mirror the expected theoretical probabilities. However, this tends to apply to large sample sizes, as small samples are prone to deviations and may not accurately reflect the overall population's characteristics.
Due to randomness and variability, a small sample size does not reliably indicate the true properties of a population. Whereas, larger sample sizes reduce sampling error, making it more likely that the sample mean will approximate the population mean (μ). The central limit theorem supports this by showing that with a larger sample size (n), the distribution of sample means approaches a normal distribution and their mean gets closer to μ.
However, it's important to note that there are no strict rules of thumb for what constitutes a sufficiently 'large' sample size, as it highly depends on the specific context, variability, and aims of the study.