first quarter - holy angel university · grade 11: first semester syllabus in statistics and...

Grade 11: First Semester Syllabus in Statistics and Probability | 1

SENIOR HIGH SCHOOL

BASIC EDUCATION DEPARTMENT

Holy Angel University

Angeles City

SYLLABUS IN STATISTICS AND PROBABILITY

SUBJECT DESCRIPTION: The learner demonstrates understanding on 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.

FIRST QUARTER

CONTENT STANDARD: The learner demonstrates understanding of key concepts of measures of random variables, probability distributions, normal probability distribution, concepts of sampling, sampling distributions of the sample means, estimation of the sample mean and population proportion.

PERFORMANCE STANDARD: The learner able to apply an appropriate random variable for a given real-life problem (such as indecision making and games of chance), accurately formulate and solve real-life problems indifferent disciplines involving normal distribution, apply suitable sampling and sampling distributions of the sample mean to solve real-life problems indifferent disciplines, and estimate the population mean and population proportion to make sound inferences in real-life problems in different disciplines.

TIME FRAME TOPICS LEARNING COMPETENCIES ASSESSMENT

WEEK 1

Classroom Orientation

o Orientation on Policies Relating to Scholastic Work and Policies Relating to Standards of Conduct on

The learner… 1. recognizes the do’s and don’ts of the school,

and the behavior that is/are expected from them.

2. identifies the scope and sequence, grading

Formative:

o Getting-to-Know-You o Who am I? o Recitation

Summative:


Campus o Orientation of the

Subject Matter, Scope and Sequence, Grading System, and Requirements

Counting Techniques o Tree Diagram o Fundamental

Counting Principle o Permutation o Combination

Values:

In probability, there are several ways on how to compute for the arrangement and combination of things; however, there is one technique which you will yourself comfortable to use with and solve the given problem easily. Likewise in life, there are a lot of challenges that you will be facing and there are of ways on how to overcome them. Nonetheless, it is still you who will be deciding to which advice and help you will use from your significant others to successfully surpass this

system, and requirements for Math 11: Statistics and Probability.

3. Enrichment: determines the number of outcomes in a sequence of events using a tree diagram.

4. Enrichment: uses the addition and

multiplication rules in finding the total number of

outcomes in a sequence of events.

5. Enrichment: finds the number of ways r can be

selected from n objects using the permutation

rules.

6. Enrichment: finds the number of ways r

objects can be selected form n objects without

regard to order using the combination rule.

7. Enrichment: applies the counting principles in

solving real-life problems.

o Reaction Paper

o LAS 1: Counting Techniques

o Quiz 1 – 1


problem.

WEEK 2

Computing Probabilities

o Sample Spaces and

Events o Simple Probability o Conditional Probability

Random Variables and Probability Distribution

o Discrete Probability

Distributions Values: o Probability helps you

determine how these events are related and how they can affect one another, including likelihood of occurrence. So in life, you must be careful in every decision you make for it can affect the future that you are planning to have and for you not to have regrets with the things you’ve done in the past.

o In Discrete Probability

The learner… 1. Enrichment: identifies sample spaces and

determines the probability of an event using classical or empirical probability.

2. Enrichment: determines the probability of compound events using the (a) addition rules and (b) multiplication rules.

3. Enrichment: finds the conditional probability of an event.

4. Enrichment: applies the Bayes’ theorem to determine the probability of an event.

5. M11/12SP-IIIa-1: illustrates a random variable

(discrete and continuous).

6. M11/12SP-IIIa-2: distinguishes between a discrete and a continuous random variable.

7. M11/12SP-IIIa-3: finds the possible values of a random variable.

8. M11/12SP-IIIa-4: illustrates a probability

distribution for a discrete random variable and

its properties.

9. M11/12SP-IIIa-5: constructs the probability

mass function of a discrete random variable and

its corresponding histogram.

10. M11/12SP-IIIa-6: computes probabilities

Formative:

o Board work o Seat work o Recitation

Summative:

o LAS 2: Computing Probabilities

o LAS 3: Discrete Probability Distributions

o Quiz 1 – 2


Distribution, it is very important to make a table that gives a list of probability values along with their associated value in the range of a discrete random variable which can be used to represent and solve problems concerning the randomness of an event in the real world. Similar to the tasks that you need to accomplish in your everyday living, it is very important for you to budget your time wisely and make a schedule for you to have pattern or system about the things that you need to finish for you to do them all properly with great quality.

corresponding to a given random variable.

WEEK 3

Random Variables and Probability Distribution

o Mean, Variance and Standard Deviation of a Discrete Random Variable

The learner… 1. M11/12SP-IIIb-1: illustrates the mean and

variance of a discrete random variable. 2. M11/12SP-IIIb-2: calculates the mean and the

variance of a discrete random variable.

Formative:


Summative:


The Binomial Distribution and Other Discrete Probability Distributions

o Binomial Experiment o Binomial Probability

Distribution o Mean, Variance, and

Standard Deviation of a Binomial Distribution

o Poisson Distribution o Geometric Distribution o Hypergeometric

Distribution Values: o When faced with a

situation where there are only two outcomes and many tries are done, it is helpful to know the average number of achieving success. This gives us foresight and anticipation of the what-ifs of life, as well as the drive to pursue success.

o In life, a foresight of

success happening in a certain trial gives a sense of security and satisfaction. Thus, it is important to know the

3. M11/12SP-IIIb-3: interprets the mean and the variance of a discrete random variable.

4. M11/12SP-IIIb-4: solves problems involving

mean and variance of probability distributions. 5. Enrichment: states the properties of a binomial

experiment. 6. Enrichment: finds the exact probabilities of X

successes in n trials of a binomial experiment 7. Enrichment: finds the mean, variance,

standard deviation of the variable in a binomial distribution.

8. Enrichment: determines probabilities for

outcomes of variables using the Poisson, geometric, and hypergeometric distributions.

9. Enrichment: solves real-life problems using the

binomial, Poisson, geometric, and hypergeometric distributions.

o LAS 4: Mean, Variance and Standard Deviation of a Discrete Random Variable

o LAS 5: The Binomial Distribution and Other Discrete Probability Distributions

o Quiz 1 – 3


number of trials until success is achieved, or even the probability that there is success after a number of trials.

WEEK 4

Normal Distribution

o The Normal Random Variable

o Properties of the Normal Distribution

o The Standard Normal Distribution

o Linear Interpolation

o Finding Percentiles or Z-scores

o Standardizing Any Normal Distribution

Values:

In life, you need to standardize the different things that you do. You should always follow the rules and regulations that your environment has and should not settle for mediocrity for you to have harmonious relationship

The learner… 1. M11/12SP-IIIc-1: illustrates a normal random

variable and its characteristics.

2. M11/12SP-IIIc-2: constructs a normal curve.

3. M11/12SP-IIIc-3: identifies regions under the

normal curve corresponding to different

standard normal values.

4. M11/12SP-IIIc-4: converts a normal random

variable to a standard normal variable and vice

versa.

5. M11/12SP-IIIc-d-1: computes probabilities and

percentiles using the standard normal table.

Formative:


Summative:

o LAS 6: - The Standard Normal

Distribution

o LAS 7:

- Linear Interpolation - Finding Percentiles or Z-

scores - Standardizing Any Normal

Distribution

o Quiz 1 – 4

Performance Task:

o “Math is Fun”


with other people.

WEEK 5

FIRST MID - QUARTER EXAMINATION

WEEK 6

Sampling and Sampling Distributions

o Introduction to Sampling Theory

o The Sampling Distributions

Values:

In sampling distributions, a small change in an element can have a drastic effect on the value of the statistic. Similarly, a minute change in a single member of a group can significantly affect the whole group – whether positively or negatively. It only implies that in decision-making, you should be mindful of your actions for it can affect your future plans and the path that you will

The learner… 1. Enrichment: defines and

differentiates population from sample.

2. M11/12SP-IIId-2: illustrates random sampling

3. M11/12SP-IIId-3: distinguishes

between parameter and statistic. 4. Enrichment: illustrates the other

probability sampling techniques. 5. Enrichment: explains the different

non-probability sampling techniques. 6. Enrichment: defines and illustrates sampling

distributions. 7. Enrichment: computes the mean and standard

error of a sampling distribution. 8. M11/12SP-IIId-4: identifies sampling

distributions of statistics (sample mean).

Formative:


Summative:

o LAS 8: Introduction to Sampling Theory

o LAS 9: The Sampling Distribution

o Quiz 1 – 5


have in life.

9. M11/12SP-IIId-5: finds the mean and variance

of the sampling distribution of the sample mean.

WEEK 7

Sampling and Sampling Distributions

o Central Limit Theorem

Values:

The Central Limit Theorem describes the normality of the distribution of sample means taken from a population that is not normally distributed. Many problems in real life involving the formation of samples and small groups can be modeled and solved using the central limit theorem. Similar in life, as you explore different opportunities and experiences, the bigger and greater the chance of developing and enhancing things that you possess.

The learner… 1. M11/12SP-IIIe-1: defines the sampling

distribution of the sample mean for normal population when the variance is:

(a) known (b) unknown

2. M11/12SP-IIIe-2: illustrates the Central Limit

Theorem. 3. M11/12SP-IIIe-3: defines the sampling

distribution of the sample mean using the Central Limit Theorem.

4. M11/12SP-IIIe-f-1: solves problems involving

sampling distributions of the sample mean.

Formative:


Summative:

o LAS 10: The Central Limit Theorem

o Quiz 1 – 6

WEEK 8

Estimation of Parameters

Basic Concepts on Estimation

o Properties of a Good

The learner… 1. M11/12SP-IIIf-2: illustrates point and interval

estimations. 2. M11/12SP-IIIf-3: distinguishes between point

Formative:



Estimator

o Point Estimation

o Interval Estimation

o Estimating the Mean of a Normal Population with Known Variance

o Estimating Population Mean Using a Large Sample: Applying the Central Limit Theorem

o Estimating the Mean of a Population with Unknown Variance using a Small Sample

o Estimating Population Means Using the T-Distribution

Values:

An estimator is used to make approximations about the population parameter. Like all approximations made in the real world setting, an estimate needs to be as close as possible to the actual value of the parameter being estimated. In life, estimation can be

and interval estimation. 3. M11/12SP-IIIf-4: identifies point estimator for

the population mean. 4. M11/12SP-IIIf-5: computes for the point

estimate of the population mean.

5. M11/12SP-IIIg-1: identifies the appropriate form

of the confidence interval estimator for the

population mean when:

(a) the population variance is known, (b) the

population variance is unknown, and (c) the Central

Limit Theorem is to be used.

6. M11/12SP-IIIg-2: illustrates the t- distribution.

7. M11/12SP-IIIg-3: constructs a t-distribution.

8. M11/12SP-IIIg-4: identifies regions under the t-

distribution corresponding to different t-values.

9. M11/12SP-IIIg-5: identifies percentiles using

the t- table. 0

Summative:

o LAS 11: - Point Estimation - Interval Estimation

o LAS 12: - Estimating the Mean of a

Population with Unknown Variance using a Small Sample

- Estimating Population Means Using the T-Distribution

o Quiz 1 – 7


compared to judging the things around us. However, when judging things, you should always make sure that you have enough information and knowledge about them to promote accuracy and fairness and have a successful and useful judgment.

WEEK 9

Estimation of Parameters Estimating Population

Proportions

o The Sample Proportion as a Point Estimator

o Probabilities Involving Distribution of Sample Proportions

o Estimating the Population Proportion

o Confidence Interval to Estimate the Difference Between Two Population Proportions

Estimating Population

The learner… 1. M11/12SP-IIIh-1: computes for the confidence

interval estimate based on the appropriate form

of the estimator for the population mean.

2. M11/12SP-IIIh-2: solves problems involving confidence interval estimation of the population mean.

3. M11/12SP-IIIh-3: draws conclusion about the

population mean based on its confidence interval estimate.

4. M11/12SP-IIIi-1: identifies point estimator for

the population proportion. 5. M11/12SP-IIIi-2: computes for the point

estimate of the population proportion. 6. M11/12SP-IIIi-3: identifies the appropriate form

of the confidence interval estimator for the population proportion based on the Central

Formative:


Summative:

o LAS 13: - The Sample Proportion as

Point Estimator - Probabilities Involving

Distributions of Sample Proportions

- Estimating the Population Proportion

o LAS 14: - Confidence Interval to

Estimate the Population Variance

o Quiz 1 – 8

Performance Task:


Variance

o Characteristics of the Chi-square Distribution

o Confidence Interval to Estimate the Population Variance

Values:

Before making the decision in your life, you should consider all the factors that might affect the outcome that you wanted. Being open-minded to the suggestions of other people is also a must for you to have a result that is beneficial or favorable to you and to the community.

Limit Theorem. 7. M11/12SP-IIIi-4: computes for the confidence

interval estimate of the population proportion. 8. M11/12SP-IIIi-5: solves problems involving

confidence interval estimation of the population proportion.

9. M11/12SP-IIIi-6: draws conclusion about the

population proportion based on its confidence interval estimate.

10. Enrichment: identifies the appropriate form of

the confidence interval estimator for the population variance.

11. Enrichment: computes the confidence

interval estimate of the population variance. 12. Enrichment: solves problems involving

confidence interval estimation of the population variance.

13. Enrichment: draws conclusion about the population variance based on its confidence interval estimate.

o “The Brochure-Reviewer Making”

WEEK 10

FIRST QUARTER EXAMINATION


SECOND QUARTER

CONTENT STANDARD: The learner demonstrates understanding of key concepts of tests of hypotheses on the population mean and population proportion and demonstrates understanding of key concepts of correlation and regression analyses.

PERFORMANCE STANDARD: The learner is able to perform appropriate tests of hypotheses involving the population mean and population proportion to make inferences in real-life problems in different disciplines and perform correlation and regression analyses on real-life problems indifferent disciplines.

TIME FRAME TOPICS LEARNING COMPETENCIES ASSESSMENT

WEEK 11

Estimation of Parameters Length and Sample Size of

a Confidence Interval

o Length of a Confidence Interval

o Sample Size Values:

The length of confidence interval is an important consideration in estimation. It is dependent on three factors—confidence level, population or sample standard deviation, and sample size. Similar to life, confidence of an individual depends on the experiences and people he/she encounters; thus, it is

The learner… 1. M11/12SP-IIIj-1: identifies

the length of a confidence

interval.

2. M11/12SP-IIIj-2: computes for the length of the confidence interval.

3. M11/12SP-IIIj-3: computes

for an appropriate sample size using the length of the interval.

4. M11/12SP-IIIj-4: solves

problems involving sample size determination.

Formative:

o Seat work o Recitation

Summative:

o LAS 1: Length and Sample Size of a Confidence Interval

o Quiz 2 – 1


important for a person to explore things and opportunities that might come on his/her way for him/her to have and develop a strong attitudes and personalities which he/she can use in the everyday life.

WEEK 12

Tests of Hypothesis The Language of

Hypothesis Testing

o Inferential Statistics and Hypothesis Testing

o Hypothesis Testing Hypothesis Test

Concerning Means

o Tests Concerning the Population Mean

Values:

Statistics is not only concerned with describing a set of data through observations and experiments. The heart of statistics is actually the creation of inferences or meaningful generalizations about a given set of data or population. Just like hypothesis testing, we

The learner… 1. Enrichment: states and

discusses the steps in hypothesis testing

2. M11/12SP-IVa-1:

illustrates: (a) null hypothesis (b) alternative hypothesis (c) level of significance (d) rejection region; and (e) types of errors in

hypothesis testing.

3. Enrichment: differentiates

directional test from non-directional test.

4. M11/12SP-IVa-2: calculates

the probabilities of committing a Type I and Type II error.

5. Enrichment: determines the

power of a test. 6. M11/12SP-IVa-3: identifies

Formative:

o Recitation o Seatwork

Summative:

o LAS 2: Test Concerning the Population Mean

o Quiz 2 – 2


need to follow steps which can be helpful for us to come up with a better decision. Life is a series of decision making and the decisions we make every day affect the result that we may have in the future.

the parameter to be tested given a real-life problem.

7. M11/12SP-IVb-1: formulates

the appropriate null and

alternative hypotheses on a

population mean.

8.M11/12SP-IVb-1: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

WEEK 13

Tests of Hypothesis Hypothesis Test

Concerning Means

o Tests on the Difference of Two Population Means

Values:

Sometimes, researchers deal with describing and testing hypotheses that involve

The learner… 1. M11/12SP-IVc-1: 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

2. M11/12SP-IVd-1: computes

Formative:


Summative:

o LAS 3: Tests on the Difference of Two Population Means

o Quiz 2 – 3


not just a single group of data. Instead, they study two groups of data to compare them in order to see if there is significant difference between them. Sometimes, we make judgments based only on the physical or observable aspects of one thing. That is why, often times, we are ending up with a wrong judgment or decision. With these matters, we should realize that comparing the physical aspects alone is not enough to have a better and significant result. Thus, critical thinking has an important role when it comes to these situations.

for the test-statistic value

(population mean).

3. M11/12SP-IVd-2: draws conclusion about the population mean based on the test-statistic value and the rejection region.

WEEK 14

Tests of Hypothesis Hypothesis Test

Concerning Proportions

o Hypothesis test for a Population Proportion

Values:

Using the z-test, few subjects can be analyzed in order to make valid predictions about a certain proportion related to a large group.

The learner… 1. M11/12SP-IVe-1: solves

problems involving test of hypothesis on the population mean.

2. M11/12SP-IVe-2: formulates

the appropriate null and alternative hypotheses on a population proportion.

3. M11/12SP-IVe-3: identifies

the appropriate form of the test – statistic when

Formative:


Summative:

o LAS 4: Hypothesis Test Concerning Proportions

o Quiz 2 – 4

Performance Task:

o “Just Paint It On”


Likewise in life, you should act like z-test in taking things you have in your environment. You should always take things one at a time; you should not rush your decisions and actions and be careful in every move you do for you not to have regrets afterwards. In the end, it is always you who will take full responsibility of all the actions that you made in life.

theCentral Limit Theorem is to be used.

4. M11/12SP-IVe-4: identifies

the appropriate rejection

region for a given level of

significance when the Central

Limit Theorem is to be used.

WEEK 15 SECOND MID - QUARTER EXAMINATION

WEEK 16

Test of Hypothesis Hypothesis Test

Concerning Proportions

o Hypothesis on the Difference of Two Proportion

Values:

Making comparisons about two large groups in terms of percentages or proportions is sometimes necessary. In such cases, a modified form of the z-test is applied. In life, we cannot avoid to compare between things especially when we are

The learner… 1. M11/12SP-IVf-1: computes

for the test-statistic value (population proportion).

2. M11/12SP-IVf-2: draws

conclusion about the population proportion based on the test-statistic value and the rejection region.

3. M11/12SP-IVf-g-1: solves

problems involving test of hypothesis on the population proportion.

Formative:


Summative:

o LAS 5: Hypothesis on the Difference of Two Proportions

o Quiz 2 – 5


in the state of confusion. However, because we want to escape such scenarios we make decisions just to get out of it. This is when hypothesis testing becomes helpful, for it reminds us that a process of analyzing the situation is an important thing for us to have a better result of our decision.

WEEK 17

Correlation and Regression Analyses Hypothesis Test

Concerning Variances

o The Chi-Square Statistic o Critical Values of Chi-

Square o Hypothesis test for a

Population Variance

Values:

Chi-square analysis

compares the counts of two

categorical variables to tell you

if a relationship exists between

the variables or not. It also

shows the effect of one

variable to the other. Just like

chi square analysis, life needs

The learner… 1. Enrichment: identifies the

parameter to be tested given a real-life problem.

2. Enrichment: identifies the

appropriate form of the test statistic to use.

3. Enrichment: identifies the

appropriate rejection region for a given level of significance.

4. Enrichment: formulates the

appropriate null and alternative hypotheses on population variances.

5. Enrichment: computes the

test statistic value. 6. Enrichment: draws a

conclusion about a

Formative:


Summative:

o LAS 6: Hypothesis Test Concerning Variances

o Quiz 2 – 6


to set critical values which are

represented by the limitations

you have. By setting these

limitations, you will know if the

actions you make are still

acceptable by the boundary

that you have set for yourself.

Thus, these limitations can

help you make a good decision

in your life.

population variance based on the test statistic value and the rejection region.

7. Enrichment: solves

problems involving test of hypothesis on the population variance.

WEEK 18

Correlation and Regression Analyses Linear Correlation

o Nature of Bivariate Data: Dependent and Independent Variables

o Displaying Relationships Using Scatter Plots

o Interpreting Scatter Plots o Measuring Linear

Association: Correlation

Values:

Usually, you can classify statistical data based on the number of variables consideration. When a study involves only one variable, it is called univariate data. And when it examines relationship

The learner… 1. M11/12SP-IVg-2: illustrates

the nature of bivariate data. 2. M11/12SP-IVg-3: constructs

a scatter plot. 3. M11/12SP-IVg-4: describes

shape (form), trend (direction), and variation (strength) based on a scatter plot.

4. M11/12SP-IVh-1: estimates

strength of association

between the variables based

on a scatter plot.

5. M11/12SP-IVh-2: calculates the Pearson’s sample

Formative:

o Recitation o Seatwork o Boardwork

Summative:

o LAS 7: Linear Correlation

o Quiz 2 – 7


between two variables (independent and dependent) it is classified as bivariate data. In the real-world context, independence is self-reliance while dependence is support seeking. This is the same for independent and dependent variables. These two variables are counted or treated differently but they can affect each other’s result or situation.

correlation coefficient. 6. M11/12SP-IVh-3: solves

problems involving correlation analysis.

WEEK 19

Correlation and Regression Analyses Linear Regression Analysis

o The Regression Line o Equation of the

Regression Line o Coefficient of

Determination o Standard Error of

Estimate for the Predicted Value of the Dependent Variable

Values:

The regression line, also called line of best fit, is the line drawn through a scatter plot which can be used to find the direction of the association between the two variables. A

The learner… 1. M11/12SP-IVi-1: identifies

the independent and

dependent variables.

2. M11/12SP-IVi-2: draws the best-fit line on a scatter plot.

3. M11/12SP-IVi-3: calculates

the slope and y-intercept of the regression line.

4. M11/12SP-IVi-4: interprets

the calculated slope and y-intercept of the regression line.

5. M11/12SP-IVj-1: predicts the

value of the dependent variable given the value of the independent variable.

Formative:

o Recitation o Seatwork o Boardwork

Summative:

o LAS 8: Linear Regression Analysis

o Quiz 2 – 8

Performance Task:

o “The iMovie Project”


person’s life is full of opportunities, experiences and success; and these things can be compared to the dots of the scattered plot. Because of these opportunities, we can create or draw our line of best fit which can be compared to our strengths or the things that best describe us in life. And so, with these strengths, people can make a good association or judgment to us.

6. M11/12SP-IVj-2: solves

problems involving regression analysis.

7. Enrichment: calculates and

interprets the coefficient of determination and the standard error of prediction of the linear regression line.

WEEK 20

SECOND QUARTER EXAMINATION

first quarter - holy angel university · grade 11: first semester syllabus in statistics and...

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