***Basic techniques involved in working with data sets. These techniques include
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Question
***Basic techniques involved in working with data sets. These techniques include basic summation principles, graphing data, and analyzing data with statistical techniques.*The goal for this learning lab is for you to develop a sense of how the size of a sample influenced the shape of the distribution of a dataset. The relationship between sample size and the shape of the distribution is captured by the Central Limit Theorem.*
1a. How does the size of a sample influence the shape of the distribution?
1b. How does the number of samplings (i.e. the number of samples drawn) influence the shape of the distribution?
Explanation / Answer
From Wikipedia: In probability theory, the central limit theorem (CLT) states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. So basically for 1a), as the number of samples (n) increase, the distribution of the samples become more and more uniform, both in terms of the sample mean (µ), and the sample standard deviation (s^2). Thus, the resulting shape of the distribution would be what we refer to in the statistical worlds as the "Bell-Shaped" distribution, with even tails on both the minimum and maximum sides of the distribution graph. As for part 1b), number of sampling refers to the number of samples one picks each time out of the sampling population, thus, the larger the sampling size, the narrower the final distribution graph. The mean does not change, but the sample standard deviation decreases with larger sampling sizes. Hence the narrowing of the distribution graph.
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