Activity 1: Perform what is being asked. Follow the steps indicated in the first column of the table to complete the activity.

Situation 1: 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

Situation 2: Mark is conducting a survey on Senior High School students who are active on environmental activities on their community. Given a population consisting of the following measurements (x) 2, 8, 11, 7, and 3. Suppose that samples of size 2 are drawn from the population. Compute the mean and variance of the sampling distribution of the sample mean.

Steps Illustration/Solution 1. Compute the mean of the Formula: population H. (1) H= = = The mean of the population is 2. Compute the variance of the X (a) ( x - 1 ) (b) ( x - 1)? population of (a) Subtract each measurement by the computed population mean ( x - H ) (b) Square the results obtained in (a) then add. Divide the sum by the frequency of measurements to get the value of the population variance. (2) (2 = [(xmuji N So, the variance of the population is 3. Determine the number of (3) Use the formula #Cne "(N-u)1 possible samples of size n = 2. 4. List all possible samples and Samples of Size 2 (4) Mean (4) their corresponding means, 5. Construct the sampling (5) Sampling Distribution of Sample Means distribution of the sample means, Sample Mean (X) Frequency ( Probability P(R) TotalD. Compute the moun of the Sample Mean sampling distribution of the sample (X) Probability PCX) (al (X) . P(X) manno, Follow thono stopn: a. Multiply the sample mean by tho corresponding probability. b. Add thur results. Total told. (6) ply = =[(X) . POO] 7. Compute the variance of the ICT onmpling distribution of the sample Alean (X) P(X) Bampla Probability (X - ) (x-1)2 x-y mann. Follow thane stopn n. Subfraal the population mean from each aampla mean. b. Square the difference. a. Multiply the reaulta by the corresponding probability. d. Add tho reaulto. Total (7) ay = ELP(X) . (X - 1)'] -_ ground So, the variance of the sampling distribution of sample means 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? followin munnly the values of the following variables fif there