3. If we will continue to increase the number of students, what do you think will the shape of the graph be? Answers: 1. The frequency polygon of each frequency distribution. Graph 3. Graph 1 Graph 2 er of Stud 4 5 6 7 8 9 10 11 12 13 14 15 Score, X Score, X 2. Computing for the mean, median and mode of each given distributions, we will realize that the resulting values are equal. Since these measures are equal, they all lie at one point. That is, at the center of the graph. 3. If we will continue to increase the number of students then in the long run, we can approximate the graph to the shape of a bell. In reality, if a distribution contains a very large number of cases with equal measures of central tendency values, then the distribution is symmetrical* and the skewness* is 0. In statistics, it is called normal distribution or normal curve (Rene, et al. 2015). In specific sense, it is called a normal probability distribution whenever the frequencies are converted to probabilities. What's New Activity 1: The data have an average of 59.15 and a standard deviation of 17.856. Guide Questions: 1. Graph the data using probability histogram 2. List all your observations about the graph. What Is It Now, to understand the nature of normal distributions, let us learn more about the properties of a normal probability distribution. There are six properties of normal distributions and these are the following: 1. The curve of the distribution is a bell-shaped. 2. The curve is symmetrical about the mean. This means if we will cut the curve about the mean, we will have balanced proportions of the halves. Specifically, we say that one is a reflection of the other. Meaning, the qualities exhibited by one are the same qualities exhibited by the other. 3. The mean, median and mode are of equal values and when sketched, they coincide at the center of the graph. This means that the mean, median and mode of the given distribution are located at exactly one point since their values are equal, and they are located at the center the graph which indicates the highest peak of the curve. Mean = Median = Mode 4. The width of the curve is determined by the standard deviation of the distribution. The curve considered at the left side defines a standard normal curve. A standard normal curve is a normal probability distribution that has mean value equal to 0 and standard deviation equal to 1 . width of the curve This property explains that the standard normal curve is used as a guide for distributions which has mean value not equal to 0 and standard deviation not equal to 1