Assessing Normality – A Classroom Note XXXXXXXXXXBy XXXXXXXXXXDr. Jack Alexander XXXXXXXXXXMiami Dade College ABSTRACT: Most courses in beginning statistics do cover the Normal Distribution. However,...

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Assessing Normality – A Classroom Note By Dr. Jack Alexander Miami Dade College ABSTRACT: Most courses in beginning statistics do cover the Normal Distribution. However, these courses tend to ignore or give minimal treatment to Assessing Normality. Having taught statistics for many years, it is my considered view, that the course would be strengthened if this assessment would be included. This paper illustrates how the use of Stemplots and Histograms along with the Empirical Rule gives us a straightforward strategy for determining closeness to normality. KEYWORDS: I. Normal Distribution II. Stemplot III. Histograms IV. Empirical Rule V. Assessment AMS Subject Classification: 62 – 07 ASSESSING NORMALITY – A CLASSROOM NOTE By Page 2 Dr. Jack Alexander Miami Dade College INTRODUCTION: Beginning statistics courses typically will include the study of the Normal Distribution. This endeavor will demand that students learn how to read probability values for both positive and negative standard deviations above and below the mean from prepared normal tables. What is not usually discussed is how to assess whether a given set of data is, in fact, Normal. In the view of this writer, the course would be enhanced if Assessing Normality where included. This paper presents a straightforward procedure for assessing normality using an arranged Stemplot, a Histogram, and the requirements of the Empirical Rule. Narrative: Many populations from the real world have normal distributions. This is particularly true for large populations. For example, the heights of adult males in any relatively large community could be modeled by the normal distribution. A Normal Distribution is bell-shaped. It turns out that about 68% of values under this bell shape lie within one standard deviation (positive or negative) of the mean. Further, about 95% of values lie within two standard deviations (positive or negative) of the mean. And, about 99.7% of values lie within three standard deviations (positive or negative) of the mean. This phenomenon is called the Empirical Rule and is illustrated in Figure 1 below. Page 3 Figure 1 (The Empirical Rule) . * . * | * * | * * | | | * * | 34 % | 34 % | * * | | | * * | 13.5 % | | | 13.5 % | * ---------------------------------------------------------------------------------------------------------------------- |---------------- 68% ---------------| |--------------------------------- 95 % ----------------------------------| |--------------------------------------------------- 99.7 % -------------------------------------------------| In addition to the Empirical percentages (68%, 95%, 99.7%), a Normal distribution will have the same mean, median and mode. To demonstrate procedures for assessing normality, we will use the data set given in Table 1 below. This table gives the ages of 76 actresses at the time they won Oscars.
Apr 13, 2021
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