Final answer:
The difference between the sample mean (M) and the population mean (μ) arises from sampling variation or random sampling error, typical in statistical studies when a sample is drawn from a population.
Step-by-step explanation:
The difference between M and μ is due to the sampling variation or random sampling error.
In any statistical analysis, especially when dealing with sample data, we expect some differences from the true population parameters due to random chance. The sample mean (M) being slightly different from the population mean (μ) is an example of sampling variation, which is the effect of chance fluctuations that naturally occur when a sample is drawn from a population. Although the sample is selected randomly and should be representative of the population, each sample will likely have different mean values. A standard deviation (s) in the sample slightly different from the population standard deviation (sigma or σ) is also common.
When collecting data from a randomly selected sample, the calculated mean will not perfectly match the true population mean due to this sampling variation. The Law of Large Numbers indicates that as the sample size (n) increases, the sample mean is expected to get closer to the population mean. However, in smaller samples, such as the one with 25 children, the chances of a larger discrepancy are higher, reflecting the natural variability in the data.