(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 12, No. 5, 2021 An Interactive Tool for Teaching the Central Limit Theorem to Engineering Students Anas Basalamah Department of Computer Engineering Umm Al-Qura University Makkah, Saudi Arabia Abstract—The sole purpose of this paper is to guide students in particular population. It is the distribution of frequencies of learning the introductory statistical concepts, such as, probability all possible outcomes that could occur for a statistics of that distribution and the central limit theorem (CLT) in an intuitive particular population. approach through an interactive tool. When a used data has different probability distributions, this paper intends to clarify The pedagogical approach taken in this paper for teaching the notions of the CLT and the use of samples in the hypothesis CLT is different comparing to the other approaches because testing of a population by demonstrating step-by-step procedures of the features of the developed interactive tool, which creates and hands-on simulation approach. This paper discusses the an engaging environment for the students and ensures students relationship between the sample size and the nature of the participation alongside to make the understanding of the CLT sampling distribution, which is a vital element of the CLT, in clear to the students. different population distribution using the developed interactive tool. Finally, the impact of the developed interactive tool is The remaining part of this paper is organised as the fol- measured via a survey experiment that illustrated the success lowing: Section II discusses the background and motivation of of the developed tool in teaching the CLT. this research topic along with the literature review, Section III Keywords—Probability distribution; CLT; population; interac- studies the concept of the central limit theorem and different tive tool; sampling distribution probability distributions, Section IV describes the importance of the central limit theorem, Section V shows the empirical demonstration of the CLT with the help of visualization using I. INTRODUCTION the interactive web-application tool, Section VI investigates The fundamental concept of statistics field in which stu- the impact of the developed tool in teaching the CLT in the dents more often face difficulties to understand is the central classroom, and Section VII concludes the paper. limit theorem (CLT). The CLT provides an overview of using random sampling method for making an inference about any II. BACKGROUND population. Therefore, it is considered as a vital concept in To make valid statistical interference about the concept inferential statistics, a critical knowledge for any statistician, of the CLT and sampling distribution, students must get and one of the foundation concepts of any statistics course. the opportunity to draw multiple samples [2]. This paper is In [1], authors highlighted to focus on developing the ideas highly motivated by the recommendation given in [2], hence of central statistics before moving on to the set of tools and it incorporates multiple samples in simulation to clear the procedures. The CLT is one of the central ideas of statistics. logic of the CLT to the students. The simulation provides a While learning it, students get puzzled more often to interpret realistic scenario to the students for intuitively understanding the theory and implication of this important concept. This these concepts. Although, simulation is not exempt of issues paper aims to create an engaging way of teaching and learning [3], but it is the best way of teaching the CLT to the students. the theory and implication of the CLT for both teachers and students through explanation, simulation, and visualization. We In [4], [5], the authors investigated that the concept of built an web application (interactive tool) using html, css, and CLT is not only difficult for the non-math major students, javascript for generating and visualizing the uniform, normal, but also for math major students. They added that the central positively skewed, and negatively skewed distribution with limit theorem is the most vital result conveyed theorem in corresponding sampling distribution. the introductory statistic course since it includes many of the statistical inferences that are required for the later part of the Students can collaborate by selecting their desired distribu- course. Although, students are lost more often in understanding tion, sample size, and number of samples during the simulation the logic behind the CLT. Therefore, it becomes a necessity process in the class for giving them a part of the simulation presenting the concept in a intuitive way through simulation process and creating an engaging environment in the class. such that it can be easily understandable to the students. Students can select different sample size and number of sam- ples for a particular distribution that enables them observing Interactive learning experience has always been considered the changes of sampling distribution more closely with the as the most effective pedagogical tools [6], [7], [8], [9], [10], changes of these parameters. It helps the student to understand [11] and the use of interactive environment is considered as the impact of sample size on the sampling distribution. The the effective way of learning and visualizing a complex theory. sampling distribution is the probability distribution obtained There are a large number of simulation tools and online applets from a large number of samples, which are drawn from a for learning the CLT as well [12], [6]. Most of these simulated www.ijacsa.thesai.org 813 j P a g e (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 12, No. 5, 2021 environments has complex interface, requires knowledge of size the shape of the sampling distribution differs. Similar programming, and has complex procedures, which makes observation found with the number of samples. The following students less attractive to these simulation applets. The time sections discusses these phenomena in detail. spent to these applets for understanding different distributions and the CLT is comparatively higher and less engaging. The sampling distribution of any given population always follows C. The Central Limit Theorem normal distribution. To clear this concept, this paper brings all the distributions along with various sample sizes together in The central limit theorem states that the sampling distribu- a single interface without showing the background codes that tion of sufficiently large size of samples drawn with replace- helps students get the idea easily in the shortest time. This ment from a given population that has the mean µ and standard paper intends to bring a simulated interactive teaching applet, deviation σ, will form an approximated normal distribution which can be used both online and offline by the students and curve. This statement is true regardless the distribution of can meet all the above criteria. the population. Usually, a sufficiently large sample size is the samples having size of 30 or more (n ≥ 30). If the population In sum, the above stated context motivates us working on distribution is normal, the CLT is true for smaller size of the same problem and providing a more interactive method samples as well. If the population distribution is strongly of teaching CLT to the students. The interactive tool designed skewed, it may require larger size and number of samples. for the students has an interactive interface that allows the The relationship between the sample size and the shape of the students to take different size and different number of samples sampling distribution is clarified in section V. iteratively for plotting their respective sampling distribution. As a result, students get an overview on how the estimated Also, the CLT statement holds correct for the binomial means of different samples with a particular sample size get population distribution, provided that min(np; n(1 − p)) > 5, centralized and form a bell-shaped curve, which is the prin- where p is the probability of success and n is the sample ciple of the CLT. The following section investigates different size. As a result, normal probability distribution can be used to probability distribution and the concept of the CLT along with quantify uncertainty for making inferences about a population its properties. mean. III. POPULATION DISTRIBUTIONS,SAMPLING 1) Properties of CLT: There are two attribute of any distri- DISTRIBUTION, AND THE CLT bution, namely- the mean (µ) and the standard deviation (σ). The sampling distribution converges the normal distribution, A. Population Distribution when its mean isp equal to the population mean and the standardp σ= n σ n The central limit theorem states that the sampling distribu- deviation is . The standard deviation decreases by n tion of a given population forms a bell-shaped curve or follows with the increment of the sample size . normal distribution regardless the variable’s distribution in the In sum, the sampling distribution approximates the normal population. The distribution of a variable can follow different distribution with the increment of sample size and the spread of probability distributions, i.e. uniform distribution, normal dis- the distribution suppressed. These properties have significant tribution, positively skewed distribution, and negatively skewed implications, which will be discussed in the later sections of distributions