C884 Task 3

docx

School

Western Governors University *

*We aren’t endorsed by this school

Course

Subject

Statistics

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by JusticeFlowerWolverine37

1 History of the Normal Distribution The history of the normal distribution, a fundamental concept in Secondary Statistics and Probability, has roots that trace back centuries. The concept of a bell-shaped curve began emerging in the eighteenth century with the work of French mathematician and consultant to gamblers Abraham de Moivre (Libretexts). He believed that if he could find a mathematical expression for the bell-shaped curve then he would be able to solve almost any probability problem. De Moivre explored the distribution of sums of independent and identically distributed random variables, laying the groundwork for what would later be known as the central limit theorem, which states that the distribution of a sum of independent and identically distributed random variables approaches a normal distribution, regardless of the original distribution (Fewster). The central limit theorem would later be proved by French mathematician Pierre- Simon Laplace in 1810. In the nineteenth century, the normal distribution gained further research traction with the work of German mathematician Carl Friedrich Gauss who extensively studied the properties of the Gaussian distribution and its significance in describing various natural phenomena. Gauss contributed significantly to the distribution's mathematical formulation and properties, although he didn't explicitly refer to it as the "normal distribution." His work laid the groundwork for understanding the distribution of errors in astronomical observations and provided the foundation for the bell-shaped curve. Using History to Enhance Instruction Understanding the historical development of the normal distribution provides a rich background for teaching statistics and probability to secondary students. By diving into the

2 contributions of historical mathematicians such as de Moivre, Gauss, and Laplace, educators can create engaging learning opportunities. For instance, students can dive deeper into historical contexts and explore the evolution from its initial formula to its widespread applications today. This approach humanizes the topic, making it more relatable and understandable. Additionally, students can engage in activities that highlight the significance of the normal distribution in real- world data like heights, test scores, or measurements in nature. Using this hands-on approach helps students comprehend statistical concepts as well as appreciate the practical applications of the normal distribution in other fields such as biology, sociology, or economics. Overall, incorporating historical context of the normal distribution into lesson plans can make statistics more engaging, relatable, and culturally diverse for secondary students leading to a deeper understanding of this fundamental statistical concept.

3 References Fewster, Ross. “Chapter 5: The Normal Distribution and the Central Limit Theorem.” Statistics 210: Probability and Statistics. Libretexts. “7.2: History of the Normal Distribution.” Statistics LibreTexts, 23 Apr. 2022, stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Lane)/ 07%3A_Normal_Distribution/7.02%3A_History_of_the_Normal_Distribution.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

C884 Task 3

Related Documents