Sampling Distribution ofthe Sample Mean.pptx

Statistics and probability 11

1. Sampling Distribution of the Sample Mean 1

2. Is a frequency distribution using the means computed from all possible random samples of a specific size taken from a population. The means of the samples are less than or greater than the mean of the population. S AMPLING DISTRIBUTION OF SAMPLE MEANS 2

3. 1. Determine the number sets of all possible random samples that can be drawn from the given population by using the formula, , where N is the population size and n is the sample size. STEPS IN S AMPLING DISTRIBUTION OF SAMPLE MEANS 3

4. 2. List all possible samples and compute the mean of each sample. 3. Construct a sampling distribution. 4. Construct histogram of the sampling distribution. STEPS IN S AMPLING DISTRIBUTION OF SAMPLE MEANS 4

5. A population of Senior High School consists of numbers 1, 2, 3, 4, 5. Create a sampling distribution of size 3. E X A M P L E 5

6. Determine the number sets of all possible random samples that can be drawn from the given population by using the formula, , where N is the population size and n is the sample size. 2. List all possible samples and compute the mean of each sample. 6 SOLUTION

7. 7 SOLUTION

8. 3. Construct a frequency and probability distribution table of the sample means indicating its number of occurrences or the frequency and probability. 8 SOLUTION

9. 4. Construct histogram of the sampling distribution. 9 SOLUTION

10. How many different samples of size n can be obtained from the following population N sizes? 10 Independent Practice

11. A population consists of the values (1, 4, 3, 2). Consider samples of size 2 that can be drawn from this population. a. List down all the possible samples and corresponding sample mean 11 Independent Practice

12. A population consists of the values (1, 4, 3, 2). Consider samples of size 2 that can be drawn from this population. b. Construct the sampling distribution of the sample means. 12 Independent Practice

13. 1. What distribution pertains to the frequency distribution of the sample mean from all the possible random samples of a particular sample size n taken from the given population? frequency c. population b. normal d. sampling 13 QUIZ

14. 2. Which of the following is NOT a step in creating sampling distribution of the sample mean? a. Compute for the standard deviation and variance of the samples. b. Construct a frequency distribution table of the sample means and probability. c. Determine the number of sets of all possible random samples. d. List all the possible random samples and solve for the sample mean of each set of samples. 14 QUIZ

15. 3 . Which of the following is the mean of sample 6, 10, 21, 25, and 28? 15.17 b. 18 c. 21.2 d. 22 15 QUIZ

16. For numbers 4-5, refer to the following set of data of a population {11, 12, 13, 14}. 4. How many different samples of size n = 2 can be drawn from the population? 6 b. 5 c. 4 d. 3 16 QUIZ

17. For numbers 4-5, refer to the following set of data of a population {11, 12, 13, 14}. 5. What is the lowest value of the sample mean in this sampling distribution? 11.5 b. 12 c. 12.5 d. 13 17 QUIZ

18. Loren was able to sell several pairs of Marikina shoes that have sizes of 4, 5, 6, 7, and 8. Consider samples of size 3 that can be drawn from this population. 18 ACTIVITY

19. 19 ACTIVITY