grade 11 Statistics and probability Week 4.pptx

Statistics

1. Statistics and Probability _ X Module 1 Module 2 Module 3 Module 4 Module 5 Module 6 Math 111 Math 112 Others

2. Statistics and Probability

3. Module 3 Module 2 Module 5 Module 1 Module 4 Third Quarter Fourth Quarter

4. Tell me the color not the word. YELLOW BROWN GREEN PURPLE WHITE BLACK GREEN BLUE YELLOW WHITE Tell me the word not the color. 1 2

5. Lesson and Coverage Learning Competencies Random Sampling

6. Lesson and Coverage Learning Competencies - illustrates a random sampling - distinguishes between parameter and statistic - identifies sampling distributions of statistics :sample mean - find the mean and variance of the sampling distribution of the sample mean - defines the sampling distribution of the sample mean for normal population when the variance is: a: known; b: unknown

7. Lesson: Random Sampling

8. Gathering useful information for a research study from large group of individuals or objects does not only involve a great deal of time, but is costly as well. It is also impractical. Sometimes, it is even impossible to collect data from the research population that is too large. To avoid this, researchers resort to sampling techniques.

9. What is Sampling? It is the process or technique of selecting a representative sample from the entire population. It is a help to the researcher to achieved unbiased results in his or her study.

10. Types of Random Sampling Simple Random Sampling Systematic Sampling Stratified Sampling Cluster Sampling

11. Simple Random Sampling It is a sampling technique in which every element of the population has the same probability of being selected for inclusion in the sample. This can be done by: lottery method fishbowl technique Slovin’s Formula: n = n – sample size N – population size  

12. Simple Random Sampling

13. You want to study the effect of social media on Grade 11 students in TLMII. You wish to use the simple random sampling technique in choosing the members of your sample. If there are 1,000 Grade 11 students in the TLMII , how many students should there be in your sample? Example Given: N = 1,000 e = 5% - ( 0.05 ) Solution: n = n = n = n = n = 285.71 n = 286  

14. Give it a try no. 1 Solve give it a try no. 1. You want to make a study on the opinions of Grade 8 students concerning the use of the Filipino language in the teaching of mathematics. There are 510 grade 8 students, how many students should there be in your sample using Table of Random Numbers?

15. Systematic Sampling It is random sampling technique in which every k th element of the population is selected until the desired number of elements in the sample is obtained. k - sample interval N - population size n - sample size  

16. Systematic Sampling

17. In a group of 250 students, how will you select a sample containing 71 students by using the systematic sampling technique? Example Given: N = 250 n = 71 Solution: k = k = k = 3.52 k = 4  

18. Give it a try no. 2 Solve give it a try no. 2 Direction: Solve the problem. In a group of 180 workers, how will you select a sample of 36 workers by using the systematic sampling technique?

19. Stratified Sampling It is a random sampling technique in which the population is first divided into strata and then samples are randomly selected separately from each stratum. In Stratified Sampling, the population is partitioned into several groups called strata, based on some characteristics like year level, gender, age, etc.

20. Stratified Sampling

21. Stratified Sampling S x n N – population size n – sample size s – elements per stratum S – sample per stratum  

22. You want to interview 200 students in your school to determine their opinion on the new school uniform. How are you going to choose your sample by using stratified sampling if there are 1, 200 students in grade 7; 1,100 in Grade 8; 1, 050 in Grade 9; 940 in Grade 10; 900 in Grade 11, and 810 in Grade 12? Example Given: n = 200 students Grade 7 = 1,200 students Grade 8 = 1,100 students Grade 9 = 1,050 students Grade 10 = 940 students Grade 11 = 900 students Grade 12 = 810 students

23. Given: n = 200 students Grade 7 = 1,200 students Grade 8 = 1,100 students Grade 9 = 1,050 students Grade 10 = 940 students Grade 11 = 900 students Grade 12 = 810 students Solution: Population No.of students per Stratum Sample per stratum Grade 7 1,200 Grade 8 1,100 Grade 9 1,050 Grade 10 940 Grade 11 900 Grade 12 810 Total N = 6,000

24. Solution: Population No.of students per Stratum Sample per stratum Grade 7 1,200 Grade 8 1,100 Grade 9 1,050 Grade 10 940 Grade 11 900 Grade 12 810 Total N = 6,000 Solution: Formula: S x n Grade 7 x 200 40 Grade 8 x 200 36.67 37 Grade 9 x 200 35  

25. Solution: Formula: S x n Grade 10 x 200 31.33 31 Grade 11 x 200 30 Grade 12 x 200 27   Solution: Population No.of students per Stratum Sample per stratum Grade 7 1,200 Grade 8 1,100 Grade 9 1,050 Grade 10 940 Grade 11 900 Grade 12 810 Total N = 6,000

26. Solution: Population No.of students per Stratum Sample per stratum Grade 7 1,200 40 Grade 8 1,100 37 Grade 9 1,050 35 Grade 10 940 31 Grade 11 900 30 Grade 12 810 27 Total N = 6,000 200

27. Give it a try no. 3 Solve give it a try no. 3 Direction: Solve the problem. Marcela, a Statistics student, wants to determine who care more about their physical appearances, the male or the female students. She wants to limit her study to the Grade 10 students. There are unequal numbers of Grade 10 students: 340 are male and 500 are female. She wants her sample to consist only of 50 students. She chooses the members of her sample using stratified sampling technique.

28. Cluster or Area Sampling In cluster sampling, the population is divided into clusters. From these clusters, a random sample of clusters will be drawn. All the elements from the sampled clusters will make up the sample. Sometimes, clusters are too large and there is a need for a second set of smaller clusters to be taken from the original clusters.

29. Cluster or Area Sampling

30. A researcher could divide the province into towns. A sample of towns will be selected using Simple Random Sampling. She or he could then divide the towns into barrios. From these towns, a sample of barrios will be selected at random. From these barrios, a sample of houses will be identified. Example

31. Types of Random Sampling Simple Random Sampling Systematic Sampling Stratified Sampling Cluster Sampling

32. Week 4 Activity Direction: Identify the type of sampling technique used by the researcher in each of the following situations: simple random sampling, systematic random sampling, stratified random sampling, or cluster random sampling. The office clerk gave the researcher a list of 500 Grade 10 students. Researcher selected every 20th name on the list. In a recent research that was conducted in a private school, the subjects of the study were selected by using the Table of Random Numbers. A researcher interviewed people from each town in the province of Albay for his research on population. A researcher is doing a research work on the students' reaction to the newly implemented curriculum in mathematics and interviewed every 10th student entering the gate of the school. A researcher who is studying the effects of educational attainment on promotion conducted a survey of 50 randomly selected workers from each of these categories: high school graduate, with undergraduate degrees, with master's degree, and with doctoral degree.

33. 6 . A researcher selected a sample of n=120 from a population of 850 by using the Table of Random Numbers. 7 . A researcher interviewed all top 10 Grade 11 students in each of15 randomly selected private schools in Metro Manila. 8 . A researcher randomly selected 10 barangays in a town for her study. She did this by writing the names of each barangays on a piece of paper which she folded and put in a bowl then she draw 10 pieces of paper from the bowl. 9 . A teacher asked her students to fall in line. He instructed one of them to select every 5 student on the line. 10 . A researcher chose the subjects of her study by selecting every k member of the population.