Central Limit Theorem and Its Applications

The purpose of this paper is to explain the central limit theorem and its application in research. Two concepts are constant companions in statistics: Central Limit theorem and distribution. The central limit theorem states that the arithmetic mean of sufficiently large number of iterations of independently random variable is the expected value of the iterations, and it is normally distributed with the mean equal to the expected value. Distribution is the probability of occurrence of a certain value within a defined range of values. The distribution type that describes the central limit theorem is the normal distribution curve. A normal distribution curve describes the probability distribution of continuous data. A normal distribution curve has the following properties: (i) it is symmetric around the point where x = mu; (ii) unimodal; (iii) it has two inflection points at x = mu - s and x = mu + s; (iv) it is log-concave in shape; and (v) it is infinitely differentiable