D. It is need to know? This module was created and written with you in mind on how to illustrate the mean and variance of a discrete random variable. This will also help you analyze real-life situated problems statistically in terms of relevant questions for you to better understand them. Your adept at analysis will help you appreciate the richness, and beauty of Statistics which will motivate you to apply to similar events and create statistical measures of your own. From this module, you will also learn how to use the given illustration to determine the mean, variance, and standard deviation of the discrete random variables. Your patience in analyzing figures and illustrations offered here in the module will help you upgrade your good pattern recognition skills as it tackles appropriate culture-based situated problems. Your ability to analyze, reason-out, and make a judgment or even decision out of statistical measures will also be practiced here. The extent of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level of students. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using. The module focused on illustrating the mean and variance of a discrete random variable. After going through this module, you are expected to: 1. learn the important concepts of mean and variance of a discrete random variable; and 2. illustrate the mean and variance of a discrete random variable. What know Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper. 1. Which of the following terms is considered as a measure of the 'central location' of a random variable? A. Probability Value B. Mean Value C. Numerical Value D. Variance 2. Which of the following notations is equivalent to the mean of the probability distribution? A. 0 B. 0Q C. R D. None of the Above 3. Which of the following notations is equivalent to the expected value of the probability distribution? A. E(X) B. & C. of D. P(x) Which of the following statements is TRUE about the standard deviation of a 4 . discrete random variable? A. It shows the spread out or dispersion of discrete random variables. B. It is obtained by multiplying the x values and their corresponding probability. C. It deals with the average or center of location of the probability distribution.how to illustrate ezAreure no better probability. D. It is the summation of the product of the square of the difference of x and its A . 4 5. Use the illustration below. What is the mean of the distribution? B. 6 C . 7 D. 8 050 0 1 2 6 7 8 9 10 6. Which of the following statements is TRUE? A. The values further away from ux have a small probability. B. The values further away from ux have a large probability. C. The values closer from ux don't have equal probability. D. The values closer from ux have equal probability. 7. Which term can be displayed the variability or the dispersions of the random variables. A. Probability Value B. Expected Value C. Mean Value D. Variance 8. What formula is used to find the variance of a discrete random variable? A. 0_x 2=> =[x.p(x)]; for all possible values of x B. of = [(x + u)2 . p(x); for all possible values of x C. of = E(x - u)2 . p(x); for all possible values of & D. o? = [(P(x) + u)2 . x ; for all possible values of x 9. Which formula is appropriate to use in finding the mean of a discrete random variable? A. E(x) = My = EX . P (x) B. E(x) = Ux = Ex+p(x) C. E(x) = Hx = EX -P(x) D. E(x) = My = Ex . p(x)2 For items 10 -11, refer to the diagram below. 8 10 2 3 5 6 7 9 1 410. What is the value of ux? A. 4 B. 5 C. 6 D. 7 1 1 How dispersed are the scores from the mean? A. 4 B. 5 C. 6 D . 7 For items 12 -13, refer to the diagram below. N ILI 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 12. What is the value of #x? A. 5 B. 7 C. 9 D. 11 13. How dispersed are the scores from the mean? A. 4 B . 6 C . 7 D. 8 For items 14-15, refer to the diagram below. 12 24 36 48 60 72 14. What is the value of Hx? A. 24 B. 36 C. 48 D. 60 15. How dispersed are the elements from the mean? A. 12 B. 24 C. 36 D. 48a large value of standard deviation (or variance) means that the distribution is spread out, with some possibility of observing values at some distance from the mean. What's More Independent Activity: Study and analyze. 40 5 10 20 30 35 15 25 1. Figure above shows the number of polo shirt sold by 5 different RTW boutiques. a. Illustrate the mean. (2 points) b. Illustrate the variance and standard deviation. (5 points) 2. From the figure below, a. Illustrate the mean or expected value. (2 points) b. Illustrate the variance and standard deviation. (5 points) 3 2 1 0 1 2 3 4 5 6 7 & 9 10 11 12 13 14 2. Compare the variance and standard deviation of the two figures provided. 3 2 T 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Figure Ameans that the distribution ving values at some distance N 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Figure B What I Have Learned 1. The mean a measure of the 'central location' of a random variable. It is the weighted average of the values that random variable X can take, with weights provided by the probability distribution. 2. The Expected Value or Mean Value of a discrete random variable x is can be computed by first multiplying each possible x value by the probability of observing that value and then adding the resulting quantities. In symbol, E(X) = MY = X1 * P(X1) + X2 * P(X2) + ... + Xn * P(Xn) = > X* P(X) 3. The Variance of a Discrete Random Variable X, denoted by o_x^2 is computed by first subtracting the mean from each possible x value to obtain the deviations, then squaring each deviation and multiplying the result by the probability of the corresponding x value, and then finally adding these quantities. 4. The formula in determining the variance of a discrete random variable is, Var(x) = 02* = 1 ( x - RX ) 2 . P( 2 ) all possible values of x 5. Mean, variance, and standard deviation can be illustrated by looking pattern and analyzing given illustrations and diagrams. 6. A small value of standard deviation (or variance) means that the dispersion of the random variable is narrowly concentrated around the mean. A large value of standard deviation (or variance) means that the distribution is spread out, with some possibility of observing values at some distance from the mean What I Can Do Family Budget Things to do: 1. Create a Table of Expenses of your family in a week. (Ask help from your Mother) 2. List the number of expenses for each day. 3. Create a graphical representation of your data gathered. 4. Base on the graphical representation you made, illustrate for the following:-4M1 9 a. mean or expected value; and b. variance and standard deviation. Share your output to the Class Group Chat through Image or Video Presentation. TASK CRITERIA Accuracy of the Data Gathered 50% Clarity and content of the visual 25% representation Originality and creativity of the 25% Presentation TOTAL 100% Assessment Multiple Choice. Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper. 1. Which of the following use the formula of (x) = Ex . p (x) ? A. Probability Distribution B. Variance of Discrete Probability Distribution C. Standard Deviation of Discrete Probability Distribution D. Mean or Expected Value of Discrete Probability Distribution 2. Among the notations below, which is equivalent to E(x)? A. Ox B. Ox C. Hz D. P (X ) 3. Which of the following statements best describe the expected value of a discrete random variable A. It is the simple average of all possible outcomes. B. It is the geometric average of all possible outcomes. C. It is the weighted average over all possible outcomes. D. It is the complex average of all possible outcomes in the distribution. To which of the following concepts refer this statement "the sum of the product of each value of a discrete random variable and its corresponding probability"? A. Probability Distribution B. Variance of Discrete Probability Distribution C. Standard Deviation of Discrete Probability Distribution D. Mean or Expected Value of Discrete Probability Distribution 5. Use the illustration below. What is the mean of the distribution? 60 10 R A. 20 B. 30 C. 40 D. 506. Which of the following statement is TRUE? A. A small value of standard deviation (or variance) indicates that the distribution of the random variable is concentrated narrowly around the mean B. A negative value of standard deviation (or variance) indicates that the distribution of the random variable is concentrated narrowly around the mean. C. The values closer from My have equal probability D. The values closer from My have equal probability. 7. Which term is calculated by summing the product of the square of the difference between the value of the random variable and the expected value, and the associated probability of the value of the random variable, taken over all of the values of the random variable, and finally taking the square root? A. Probability Distribution B. Variance of Discrete Probability Distribution C. Standard Deviation of Discrete Probability Distribution D. Mean or Expected Value of Discrete Probability Distribution 8. What another notation can be used for a variance? A. E(X) B. P(X) C. P (X) D. Var(X) 9. If the variance of a probability distribution is 2.6 grams, then what proper way to do to get the standard deviation? A. V2.6 B. (2.6)2 C. 1.61 + 2.6 D. 1.61 - 2.6 For items 10-11, refer to the diagram below. m 4 5 6 7 8 9 10 11 12 13 14 10. What is the value of fx? B. 5 C. 6 D. 7 1 1. How dispersed are the scores from the mean? A. 5 B. 6 C. 7 D. 8For items 12 -13, refer to the diagram below. 3 18 21 9 12 15 12. What is the value of ux? A. 6 B. 9 C. 12 D. 15 13. How dispersed are the elements from the mean? A . 9 B. 12 C. 15 D. 18 For items 14 -15, refer to the diagram below. 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14. What is the value of ux? A. 5 B. 7 C. 9 D. 11 15. How dispersed are the scores from the mean? A.5 B. 7 C. 9 D. 11 Additional Activities Study and analyze the figures below. 3 3 N 2 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10