MATH1280 Statistics 1 Discussion forum UNIT6
Grades 9.80/0-10
Mathematical models are used as tools to describe reality. These models are supposed to characterize the important features of the analyzed phenomena and provide insight. The normal distribution is an example of a random variable that is widely used by researchers to model real data.
Researchers often model real observations using the normal distribution, but sometimes the real distribution is a bit different from the perfect, normal distribution. List some reasons why researchers might make approximations like this and describe at least one situation when researchers should not use this approximation.
When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable can serve as a model.
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Researchers often model real observations using the normal distribution, but sometimes the real distribution is a bit different from the perfect, normal distribution. List some reasons why researchers might make approximations like this and describe at least one situation when researchers should not use this approximation. When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable can serve as a model.
The most fundamental property of the normal distribution is that the mean, mode, and median match. So the normal distribution is a tool used primarily to understand the distribution of factors within a population and to identify causes and probabilities (Yakir, 2011).
The distribution of human height is often given as a familiar example of following a normal distribution. For example, when examining the height distribution using the height data of the people published by the country, it can be expected that the average value, mode value, and median value will match according to the normal distribution. In addition, individual observations are very likely to be included in the mean and a particular standard deviation (Yakir, 2011).
But sometimes, the real distribution is a bit different from the perfect, normal distribution. One of the causes is sample bias. If there is any mechanism for partial extraction, bias can occur, and the sample can be biased. For example, when data is extracted from the people who answered the questionnaire, the target will be biased if only the respondents are analyzed because they have some intention at the time of answering the questionnaire.
When we do a survey that answers the question with an 11-point rating scale from 0 to 10 about satisfying the products, the data samples will be biased by product quality. Researchers should not use this approximation when there are such factors that bias the data, such as human subjectivity and product quality.
References
Yakir. B, (2011). Introduction to Statistical Thinking (With R, Without Calculus). Retrieved from https://my.uopeople.edu/pluginfile.php/1097279/mod_book/chapter/267923/MATH1280RInstall Notes. pdf
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