Sampling Distribution - Central Limit Theorem A histogram of the outcomes visualizes the sampling distribution: the distribution of a sample statistic over many repeated samples. We then computed the average number of marriages in each of these samples. We actually drew 1,000 samples of n = 10 respondents from our population data of 976 inhabitants. If we draw repeated samples of 10 respondents from our island population, then how much will the average number of marriages vary over such samples? One approach here is a computer simulation (the one below was done with SPSS). Like so, we can at least estimate a likely range -known as a confidence interval- for a population parameter such as an average number of marriages. The solution to the problem is to figure out how much they vary. This is basically the fundamental problem in inferential statistics: sample statistics vary over (hypothetical) samples. So what does this say about the entire population of 976 people? We can't conclude that they marry 1.1 times on average because a second sample of n = 10 will probably come up with a (slightly) different mean number of marriages. On average, the 10 respondents married 1.1 times. Since this is too time consuming, he decides to draw a simple random sample of n = 10 people. In theory, he could ask all 976 people and thus find the exact population distribution of marriages. So although the government knows, our scientist is clueless how often the island inhabitants marry. However, a social scientist doesn't have access to these data. The government has these exact population figures. These descriptives reemphasize the high skewness of the population distribution the skewness is around 1.8 whereas a symmetrical distribution has zero skewness. On average, people married some 1.1 times as shown by some descriptive statistics below. Note that the population distribution is strongly skewed (asymmetrical) which makes sense for these data. The histogram below shows the distribution of marriages over our 976 inhabitants. Other inhabitants married, divorced and remarried, sometimes multiple times. Many inhabitants never married (yet), in which case marriages is zero. The screenshot below shows part of these data.

Its government has data on this entire population, including the number of times people marry. Types of Probability Distributions: Codes, Examples Sampling Distribution - Example

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