Abstract
This simulation employed a compiler which explains the role of central limit theorem in dealing with populations that are not normally distributed. A group of 10000-data-point populations were simulated according to five different kinds of distribution: uniform, platykurtic normal, positively-skewed exponential, negatively-skewed triangular, and bimodal. Three 500-data-point sampling distributions of sample sizes of 2, 10, and 30 were created from each population. All populations and sampling distributions were displayed in histograms for analysis along with their means and standard deviations. The results verified the principles of the central limit theorem and indicated that if the population is close to normality, a smaller sample size is needed so that the central limit theorem can take effect. But if the population is far from normality, a large sample size might be required. A proportion of population was proposed for a sample size based on the simulation results. Further studies and implications are discussed.
Highlights
People all over the world were created in different heights and widths
The importance of statistics appears when researchers attempt to answer this kind of question: what is the true average length of people living in, for example, the U.S.? The first step for answering this question is to collect data relating to the lengths of American people
A sampling distribution dragged from a uniform population starts approaching the normal distribution even when the sample size is small
Summary
People all over the world were created in different heights and widths. Let’s say that hundreds of millions of men and women get together in one location such as the United States. Something is needed to serve as a clear and convenient synopsis of the heights of all people living in the U.S That could be attained by what are called statistics. The importance of statistics appears when researchers attempt to answer this kind of question: what is the true average length of people living in, for example, the U.S.? The first step for answering this question is to collect data relating to the lengths of American people. It is almost always impossible to place all American people in a line and get their lengths with perfect measurements. The practical solution here is to randomly select a representative sample from the American population and collect the lengths of all individuals included in that sample. The population must be clearly specified; otherwise the sample will be poorly drawn from the population [13]
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