Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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In a sampling distribution of the mean, what does the mean of the sampling distribution equal?

  1. The mean of the sample population

  2. The mean of the sampled population

  3. The mean of all samples taken

  4. The mean of the entire population

The correct answer is: The mean of the entire population

In a sampling distribution of the mean, the mean of this distribution is equal to the mean of the entire population. This principle is a key aspect of the Central Limit Theorem, which states that no matter what the shape of the population distribution is, the distribution of the sample means approaches a normal distribution as the sample size increases. The mean of all sample means will converge to the true population mean as more samples are taken. This means that, on average, the means computed from samples will accurately reflect the mean of the entire population from which the samples were drawn, provided that the samples are random and representative. Thus, in the context of statistical analysis and inferential statistics, this characteristic allows researchers to make generalizations about the population based on sample data.

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