Direction: Perform what is being asked. Follow the steps indicated in the first column of the table to complete the activity. In the second column, write your solution on the spaces provided. Situation: A population of PWD learners in 5 schools in a certain municipality of Quezon Province are (x) 9, 5, 6, 12, and 15. Suppose that two schools were selected as samples, determine the mean and variance of the sampling distribution of sample mean. Steps Illustration/Solution 1. Compute the mean Formula: of the population . (1) A = EX/N= The mean of the population is 2. Compute the variance the X (8) X - H b (X -)z population . (a) Subtract each measurement by the computed population mean (x- H) (2) 62 = E(X - H)? / N = (b) Square the results So, the variance of the population is obtained in (a) then add. Divide the sum by the frequency measurements to get the value of the population variance. E(x - H) / N 3. Determine the number of possible (3) Use the formula ,Ca. = N! samples of size n = 2. TIX(N-m)! 4. List all possible samples and their Samples of size 2 (4) Mean (4) corresponding means.5. Construct the (5) Sampling Distribution of Sample Means sampling distribution Sample Mean Frequency Probability of the sample means. (X (D P(X) Total ( 6. Compute the Sample Probability (a) S. Mean . Probability Mean mean of the (X) P(X (X . P(X) sampling distribution of the sample means. Follow these steps: a. Multiply the sample mean by the corresponding probability. Total (b b. Add the results. Note: S. Mean = Sample Mean (6) H2 = E[X . P(X)] H& = 7. Compute the variance of the sampling distribution Sampl Probability (b) (c) of the sample mean. e Mean S Mean (S. Mean- Probability.(S. Follow these steps: - P.Mean P. Mean) Mean-P. a. Subtract the Mean)2 population mean from ( x ) P(X) (X - H) (X - 1) 2 each sample mean. P( X) . (X-1)2 b. Square the difference. c. Multiply the results by the corresponding probability. Total (d) d. Add the results. Note: S. Mean = Sample Mean, P. Mean = Population Mean (7) Variance: of = EIP(X) . (X - 4)21= So, the variance of the sampling distribution of sample the means is 1. How did you find the activity? 2. How do you compare the mean of the sample mean and the mean of the population? 3. How does the variance of the sample mean and the variance of the population differ