Statistics Assignment: Normal Distribution, Sample Data, and Skewness

This assignment delves into the concept of normal distribution within statistics, exploring its application and relevance through an analysis of sample data. The assignment discusses how the normal distribution, a probability function, is used to model and understand data, such as the heights of 20-year-old boys, where multiple factors influence the outcome, leading to a normal distribution. The central limit theorem is highlighted to explain how sample means tend towards the population mean, which is essential for understanding data variability. The assignment then contrasts the normal distribution with the skewed distribution that can result from specific sample selections, such as boys with long hair. It explains how the skewness can appear in the data and how the mean and median values affect the shape of the distribution. The references provided support the concepts discussed, offering deeper insights into the theoretical aspects of normal distribution and related statistical analyses.

Running head: STATISTICS 1
Statistics
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STATISTICS 2
Example of a population with normal distribution
In statistics, the normal distribution is a probability function which describes how the
variable values are distributed within a population. For instance, the data for the heights 20-year
old boys are expected to be normally distributed since the occurrence of the individual scores are
based on the natural phenomena. Concisely, the data for the heights will follow the normal
(Gaussian) distribution as many genetic and environmental factors influence the heights of
individuals. The existence of the many independent factors determining the phenomenon, in
essence, the heights of the boys, the result would follow the normal distribution due to the central
limits theorem which deduces that given a sufficiently large sample sizes from a population with
finite variance. Moreover, the mean from all samples from the same people will be
approximately equal to the mean due to the central limits theorem (Bowditch, 2019).
The subset of the population
When a sample data randomly sorted from the entire population, there are high chances
that the resultant subset would not be normally distributed like the initial population. For
instance, if the boys with long hair are sorted out of the 20-year old boys, the subset is likely to
take the shape of a skewed distribution. Moreover, the distribution will be either skewed
negatively or skewed to the left if the height scores fall towards the higher side whereas the
distribution could be a postive skew when the average is higher than the median that is greater
than the mode (Thiuthad and Pal, 2019).

STATISTICS 3
References
Bowditch, A. (2019). Central limit theorems for biased randomly trapped random walks on
Z. Stochastic Processes and their Applications, 129(3), 740-770.
Thiuthad, P., & Pal, N. (2019). Point Estimation of the Location Parameter of a Skew-Normal
Distribution: Some Fixed Sample and Asymptotic Results. Journal of Statistical Theory
and Practice, 13(2), 37.