FROM MELL er going through this SSLM, you are expected to: find the mean and variance of the sampling distribution of the sample mean; (M1 1/ 12SP-IIId-5) and define the sampling distribution of the sample mean for the normal population when the variance is known and unknown. (M1 1/12SP- IIIe-1) ACTIVITIES A. LET US REVIEW 1. The following are sample data obtained from the Statistics Quiz of 22 students in Math High School in Quezon Province. Compute the mean and variance of the frequency distribution. SCORES f SCORES F 61 84 2 68 1 86 2 71 1 88 2 72 1 89 1 75 1 90 1 81 1 91 3 82 95 83 2 96 Total 22 2. Mean and Variance of the Probability Distribution Complete the table below and find the mean and variance of the given probability distribution. X P(X) X . P(X) ( X - ( ) ( X - 1 ) 2 ( X - H)2 . P( X) 0.134 2 0.231 3 0.09 0. 165 0. 112 0.07 0. 198 B. LET US STUDY Finding the Mean and Variance of the Sampling Distribution of the Sample MeanActivity 2: Read and analyze the following situations and supply the values of the following variables is any). On the third column, write known on the space provided if the situation gives or can compute the value of the variance, otherwise write unknown. Identify also the formula to be used to estimate the standard error of the mean by writing the symbols of, when the population variance is known and s, when the population variance is unknown. Situation Given Answer Standard Error Formula 1. Consider a population consisting of 1, 2, 3, 4, 5, 8, 9, and 11. Samples of size 3 are drawn from this population. 2. Given the population mean of 12, and a n = sample standard deviation of 3 in a sample size of 125 3. A population composed of ll items whose measurements are 12, 7, 9,11,8, 20, 23, 18, 13, 22, and 10. Samples of 5 items are drawn at random without replacement. 4. The owner of the drugstore chain has 100 drugstores that sell Flexcoslow, a surgical mask that prevents a person from catching liquid droplets of viruses. His operation manager said that the average drugstores in X = his chain sell 12 boxes of the Flexcoslow a day S = with a standard deviation of 2 boxes. To find out if this is true, the owner randomly selected 10 stores and found that the mean is 15 boxes with a standard deviation of 1 box. 5. The mean height of the students at Maligaya Elementary School is 137.16 cm. To find out if the statement is true, a sample of 15 students is taken from the population. The S = mean of the sample is 139.1 cm with a standard deviation of 2.23 cm. 1. How did you find the activity? 2. How does each situation differ from each other? 3. What is the difference between the two symbols of and $, in finding the standard error of the mean