CLASSROOM DEMONSTRATION FOR RANKING.pptx

The "Honor All" Certificate is a prestigious recognition that celebrates outstanding performance, dedication, and achievement in various fields, such as academics, professional endeavors, volunteer work, or personal development. It serves as a formal acknowledgment of an individual's exceptional contributions and sets them apart as role models within their respective communities. The certificate typically represents a combination of excellence, integrity, and commitment to higher standards of achievement and ethical conduct.

### Purpose of the Honor All Certificate
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1. Statistics and probability Statistics and probability

2. Dear God, Thank you for today. Thank you for all the blessings you have provided us all. Purify our thoughts and actions that can glorify you. God, we offer you today our works and studies. Help us to be attentive and obedient to our teachers, to be kind to our classmates and to be diligent in our studies. Help us focus on our hearts and minds now on what we are about to learn TODAY. This we pray AMEN…

3. HI LEARNERS, I AM ... MR. REYMART B. SALADAS HI LEARNERS, I AM ...

4. Recap…. Recap….

5. HI LEARNERS, I AM ... MR. REYMART B. SALADAS HI LEARNERS, I AM ...

6. E-RELAY…. E-RELAY…. Mechanics: Students pass an eraser around while music plays, and when the music stops, the person who is holding the eraser must answer a question. If they answer correctly, they earn a reward. This continues until all questions has been answered.

7. Question 1 When conducting an experiment, why is it important to randomly select participants from a larger population?

8. answer Random selection ensures that every individual in the population has an equal chance of being chosen,

9. Question 2 If you randomly choose 10 students from a class of 50 to answer a survey, what method ensures that each student has an equal chance of being selected?

10. answer The method is simple random sampling, where each student in the class has the same probability of being selected for the survey

11. Question 3 How can random sampling help improve the reliability of the results in a study or survey?

12. answer Random sampling helps reduce selection bias, making the sample more representative of the entire population, which increases the external validity and generalizability of the results.

13. Question 4 What is one potential issue that could arise if participants are not randomly selected in a study?

14. answer If participants are not randomly selected, the sample may be biased, leading to skewed results that do not accurately represent the larger population, which can affect the validity of the study.

15. “Finding the mean and variance of the sampling distribution of the sample mean”

16. OBJECTIVES At the end of the lesson, the students must have: calculated the mean, variance, and standard deviation of the sampling distribution of the samples means. explained the relevance of selecting a sample from a population in real life scenarios.

17. Formulas: N n - number of samples with replacement  x   x̄ . P(x̄) - mean of the sampling distribution of the sample means 3. σ 2 x  P(x̄) . (x̄ -  x ) 2 - variance of the sampling distribution of the sample means

18. Steps: 1. Determine the number of samples using the formula N n . 2. List all the possible samples and their corresponding means. 3. Construct the sampling distribution of the means.

19. 4. Compute the mean of the sampling distribution of the sample means. a. Multiple the sample mean by the corresponding probability b. Add the results

20. 5. Compute the variance of the sampling distribution of the sample means. Subtract the sample means  x from each sample x̄ . Label this as x̄   x. Square the difference x̄   x. Multiply the results by the corresponding probability. Label this as P(x̄) . (x̄ -  x ) 2 . Add the results

21. example example A population consists of three numbers (2, 4, 6). Consider all possible samples of size 2 which can be drawn with replacement from the population.

22. List all the possible samples and their corresponding means. Samples Sample Mean 2,2 2 2,4 3 2,6 4 4,4 4 4,2 3 4,6 5 6,6 6 6,2 4 6,4 5

23. Construct a sampling distribution of the means. Sample Mean x̄ Frequency Probability P(x̄) 2 1 1/9 3 2 2/9 4 3 3/9 5 2 2/9 6 1 1/9 Total 9 1

24. Compute the mean of the sampling distribution of the sample means. Sample Mean x̄ Probability P(x̄) x̄ . P(x̄) 2 1/9 0.22 3 2/9 0.67 4 3/9 1.33 5 2/9 1.11 6 1/9 0.67 Total   4

25. Compute the variance of the sampling distribution of the sample means. Sample Mean x̄ Probability P(x̄) x̄ . P(x̄) x̄ -  x P(x̄) . (x̄ -  x ) 2 2 1/9 -2 4 0.44 3 2/9 -1 1 0.22 4 3/9 5 2/9 1 1 0.22 6 1/9 2 4 0.44 Total       1.32

26. The variance is σ 2 x  P(x̄) . (x̄ -  x ) 2 = 1.32 Thus the standard deviation σ is = 1.15  

27. The class will be divided into two groups. Each group will be given with problems to be solved in 10 minutes. The group which can finish solving the problem first with correct solutions and answers will be declared as the winner. Each group must select one representative to explain the output in front. Group activity Group activity

28. Problem: A population consists of four numbers (18, 20, 22, 24). Consider all possible samples of size 2 which can be drawn with replacement from the population.

29. What have you understood about the lesson?

30. Which part of the lesson you did not understand well?

31. Were our learning objectives successfully attained?

32. What core values are reflected in our lesson?

33. To which subject area can we relate today’s topic?

34. How important is sampling in our daily lives?

35. Directions: In a one whole sheet of paper, calculate the mean, variance, and standard deviation of the sampling distribution of the sample means from a population indicated in the given problem. Problem: Consider a population consisting of 1, 2, 3, 4, & 5. Suppose samples of size 2 are drawn from this population with Replacement. What is the mean, variance, and standard deviation of the sampling distribution of sample means? Quiz …. Quiz ….

36. assignment Directions: Research other ways of finding the mean, variance, and standard deviation of the sampling distribution of the sample mean from a population. Compare the ways that you have found out to the one that we have employed in the class. Present it through a PowerPoint presentation which is to be submitted next week.

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38. THANK YOU, LEARNERS! THANK YOU, LEARNERS!

39. STATISTICS AND PROBABILITY STATISTICS AND PROBABILITY