K to 12 BASIC EDUCATION CURRICULUM SENIOR HIGH SCHOOL CORE SUBJECT
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1 Grade: 11/12 Core Subject Title: Statistics and Probability No. of Hours/Semester: 80 hours/semester Prerequisite: Core Subject Description: At the end of the course, the students must know how to find the mean and variance of a random variable, to apply sampling techniques and distributions, to estimate population mean and proportion, to perform hypothesis testing on population mean and proportion, and to perform correlation and regression analyses on real-life problems. CONTENT Random Variables and Probability Distributions Normal Distribution CONTENT concepts of random variables and probability distributions. understanding of key concepts of normal probability distribution. apply an appropriate random variable for a given real-life problem (such as in decision making and games of chance). accurately formulate and solve real-life problems in different disciplines 1. illustrates a random variable (discrete and continuous). M11/12SP-IIIa-1 2. distinguishes between a discrete and a continuous M11/12SP-IIIa-2 3. finds the possible values of a M11/12SP-IIIa-3 4. illustrates a probability distribution for a discrete random variable and its properties. 5. constructs the probability mass function of a discrete random variable and its corresponding histogram. 6. computes probabilities corresponding to a given 7. illustrates the mean and variance of a discrete random variable. 8. calculates the mean and the variance of a discrete 9. interprets the mean and the variance of a discrete 10. solves problems involving mean and variance of probability distributions. 11. illustrates a normal random variable and its characteristics. M11/12SP-IIIa-4 M11/12SP-IIIa-5 M11/12SP-IIIa-6 M11/12SP-IIIb-1 M11/12SP-IIIb-2 M11/12SP-IIIb-3 M11/12SP-IIIb-4 M11/12SP-IIIc constructs a normal curve. M11/12SP-IIIc-2 K to 12 Senior High School Core Curriculum Statistics and Probability December 2013 Page 1 of 7
2 CONTENT involving normal distribution. 13. identifies regions under the normal curve corresponding to different standard normal values. M11/12SP-IIIc converts a normal random variable to a standard normal variable and vice versa. M11/12SP-IIIc-4 Sampling and Sampling Distributions concepts of sampling and sampling distributions of the sample mean. apply suitable sampling and sampling distributions of the sample mean to solve real-life problems in different disciplines. 15. computes probabilities and percentiles using the standard normal table. 1. illustrates random sampling. 2. distinguishes between parameter and statistic. 3. identifies sampling distributions of statistics (sample mean). 4. finds the mean and variance of the sampling distribution of the sample mean. 5. defines the sampling distribution of the sample mean for normal population when the variance is: (a) known (b) unknown M11/12SP-IIIc-d- 1 M11/12SP-IIId-2 M11/12SP-IIId-3 M11/12SP-IIId-4 M11/12SP-IIId-5 M11/12SP-IIIe-1 6. illustrates the Central Limit Theorem. M11/12SP-IIIe-2 7. defines the sampling distribution of the sample mean using the Central Limit Theorem. M11/12SP-III-3 8. solves problems involving sampling distributions of the sample mean. M11SP-IIIe-f-1 Estimation of Parameters concepts of estimation of population mean and estimate the population mean and population proportion to make sound 1. illustrates point and interval estimations. M11/12SP-IIIf-2 2. distinguishes between point and interval estimation. M11/12SP-IIIf-3 K to 12 Senior High School Core Curriculum Statistics and Probability December 2013 Page 2 of 7
3 CONTENT inferences in real-life problems in different disciplines. 3. identifies point estimator for the population mean. M11/12SP-IIIf-4 4. computes for the point estimate of the population mean. M11/12SP-IIIf-5 5. identifies the appropriate form of the confidence interval estimator for the population mean when: (a) the population variance is known, (b) the population M11/12SP-IIIg-1 variance is unknown, and (c) the Central Limit Theorem is to be used. 9. illustrates the t-distribution. M11/12SP-IIIg constructs a t-distribution. M11/12SP-IIIg identifies regions under the t-distribution corresponding to different t-values. M11/12SP-IIIg identifies percentiles using the t-table. M11/12SP-IIIg computes for the confidence interval estimate based on the appropriate form of the estimator for the population mean. 13. solves problems involving confidence interval estimation of the population mean. 14. draws conclusion about the population mean based on its confidence interval estimate. M11/12SP-IIIh-1 M11/12SP-IIIh-2 M11/12SP-IIIh identifies point estimator for the M11/12SP-IIIi computes for the point estimate of the population proportion. 17. identifies the appropriate form of the confidence interval estimator for the population proportion based on the Central Limit Theorem. 18. computes for the confidence interval estimate of the 19. solves problems involving confidence interval estimation of the M11/12SP-IIIi-2 M11/12SP-IIIi-3 M11/12SP-IIIi-4 M11/12SP-IIIi-5 K to 12 Senior High School Core Curriculum Statistics and Probability December 2013 Page 3 of 7
4 CONTENT 20. draws conclusion about the population proportion based on its confidence interval estimate M11/12SP-IIIi identifies the length of a confidence interval. M11/12SP-IIIj computes for the length of the confidence interval. M11/12SP-IIIj computes for an appropriate sample size using the length of the interval. 24. solves problems involving sample size determination. M11/12SP-IIIj-3 M11/12SP-IIIj-4 Tests of Hypothesis concepts of tests of hypotheses on the population mean and perform appropriate tests of hypotheses involving the population mean and population proportion to make inferences in real-life problems in different disciplines. 1. illustrates: (a) null hypothesis (b) alternative hypothesis (c) level of significance (d) rejection region; and (e) types of errors in hypothesis testing. 2. calculates the probabilities of committing a Type I and Type II error. M11/12SP-IVa-1 M11/12SP-IVa-2 3. identifies the parameter to be tested given a real-life problem. M11/12SP-IVa-3 4. formulates the appropriate null and alternative hypotheses on a population mean. M11/12SP-IVb-1 5. identifies the appropriate form of the test-statistic when: (a) the population variance is assumed to be known (b) the population variance is assumed to be unknown; and (c) the Central Limit Theorem is to be used. M11/12SP-IVb-2 K to 12 Senior High School Core Curriculum Statistics and Probability December 2013 Page 4 of 7
5 CONTENT 6. identifies the appropriate rejection region for a given level of significance when: (a) the population variance is assumed to be known (b) the population variance is assumed to be unknown; and (c) the Central Limit Theorem is to be used. M11/12SP-IVc-1 7. computes for the test-statistic value (population mean). M11/12SP-IVd-1 8. draws conclusion about the population mean based on the test-statistic value and the rejection region. 9. solves problems involving test of hypothesis on the population mean. 10. formulates the appropriate null and alternative hypotheses on a M11/12SP-IVd-2 M11/12SP-IVe-1 M11/12SP-IVe identifies the appropriate form of the test-statistic when the Central Limit Theorem is to be used. 12. identifies the appropriate rejection region for a given level of significance when the Central Limit Theorem is to be used. 13. computes for the test-statistic value (population proportion). M11/12SP-IVe-3 M11/12SP-IVe-4 M11/12SP-IVf draws conclusion about the population proportion based on the test-statistic value and the rejection region. 15. solves problems involving test of hypothesis on the M11/12SP-IVf-2 M11/12SP-IVf-g- 1 K to 12 Senior High School Core Curriculum Statistics and Probability December 2013 Page 5 of 7
6 CONTENT CONTENT ENRICHMENT concepts of correlation and regression analyses. Correlation and Regression Analyses perform correlation and regression analyses on real-life problems in different disciplines. 1. illustrates the nature of bivariate data. M11/12SP-IVg-2 2. constructs a scatter plot. M11/12SP-IVg-3 3. describes shape (form), trend (direction), and variation (strength) based on a scatter plot. M11/12SP-IVg-4 4. estimates strength of association between the variables based on a scatter plot. M11/12SP-IVh-1 5. calculates the Pearson s sample correlation coefficient. M11/12SP-IVh-2 6. solves problems involving correlation analysis. M11/12SP-IVh-3 7. identifies the independent and dependent variables. M11/12SP-IVi-1 8. draws the best-fit line on a scatter plot. M11/12SP-IVi-2 9. calculates the slope and y-intercept of the regression line. 10. interprets the calculated slope and y-intercept of the regression line. 11. predicts the value of the dependent variable given the value of the independent variable. M11/12SP-IVi-3 M11/12SP-IVi-4 M11/12SP-IVj solves problems involving regression analysis. M11/12SP-IVj-2 K to 12 Senior High School Core Curriculum Statistics and Probability December 2013 Page 6 of 7
7 Code Book Legend Sample: M11/12SP-IIIa-1 LEGEND SAMPLE Learning Area and Strand/ Subject or Specialization Mathematics First Entry M11/12 Grade Level Grade 11/12 Uppercase Letter/s Domain/Content/ Component/ Topic Statistics and Probability SP - Roman Numeral *Zero if no specific quarter Lowercase Letter/s *Put a hyphen (-) in between letters to indicate more than a specific week Quarter Third Quarter III Week Week one a - Arabic Number Competency illustrates a random variable (discrete and continuous) 1 K to 12 Senior High School Core Curriculum Statistics and Probability December 2013 Page 7 of 7
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