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To truly grasp the concept of population mean, let's explore its role in statistics. The population mean is the average value of a key measurement if you consider every individual in a given group or population. For example, if each student's GPA in a school is added together and then divided by the total number of students, the result is the population mean GPA.

Understanding the difference between sample mean and population mean is crucial. The sample mean is an average value derived from a subset of the population, while the population mean is the average across the entire population. The population mean is a vital benchmark as it represents the true average, unaffected by sampling variations.

When your sample size equals the population size, the sample mean becomes equal to the population mean, eliminating the sampling variability. This is essential when studying the sampling distribution of a sample mean.

Sample size refers to the number of observations or data points taken from a population to form a sample. It is a critical factor that influences the reliability and accuracy of statistical analyses.

In our exercise, when the sample size equals the population size, the sampling distribution of the sample mean becomes a single value: the population mean. But what happens if the sample size is just one?

With a sample size of 1, each sampled mean is simply the data point itself. The mean directly reflects the individual's observation, making it equivalent to the population distribution. Larger sample sizes tend to result in a more normal distribution of the sample mean, whereas smaller ones, like n=1, result in a distribution that mirrors the population distribution quite closely.

GPA, or Grade Point Average, is a standard metric used to evaluate a student's academic performance. It is usually calculated by assigning numerical values to letter grades.

In the context of this problem, each student's GPA can be considered as a single data point in the entire school's population. The average of all these GPAs would give you the population mean GPA.

In statistical terms, GPA serves as a random variable that can help understand the statistical concepts of sampling and population distribution. By assessing different GPAs among students, educational institutions and other stakeholders can analyze overall academic performance and make informed decisions.

The population distribution represents how often each possible value of a variable occurs in an entire population. It shapes our expectations of the data's spread and central tendencies.

In many cases, assuming the population distribution is normal provides ease in analysis, though real-world data might display variations. In the school GPA context, each GPA is a data point in the population distribution.

If you take a very small sample size, like one student, the sampled means mimic the population distribution directly. Hence, for a sample size of 1, the sampling distribution of the mean reflects the actual population distribution, as it is based on the individual's GPA data without any aggregation or averaging effects.