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MATH7 Q4 MOD1-1 - Module
Applied Math (APMATH)
University of Santo Tomas–Legazpi
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Mathematics
Quarter 4 – Module 1
Real-Life Problems that can be
Solved by Statistics
Mathematics – Grade 7 Alternative Delivery Mode Quarter 4 – Module 1: Real-Life Problems that can be Solved by Statistics First Edition, 2020
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Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by- step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self- check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
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What I Need to Know
This module was designed and written with you in mind. It is here to help you master the Real-Life Problems that can be Solved by Statistics. The scope of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level of students. The lessons are arranged to follow the standard sequence of the course. However, the order in which you read them can be changed to correspond with the textbook you are now using.
The module is divided into two lessons, namely:
Lesson 1 – Poses Real-Life Problems that can be Solved by Statistics Lesson 2 – Formulates Simple Statistical Instrument
After going through this module, you are expected to:
- identify statistical and non-statistical question;
- identify numerical (discrete or continuous) and categorical data sets;
- pose real-life problems that can be solved by statistics; and
- formulate simple statistics instrument.
What I Know
DIRECTIONS: Choose the letter of the correct answer. Write the chosen letter on a separate sheet of paper.
What is a query that can be answered by collecting data that may vary? A. Categorical data set B. Numerical data set C. Statistics D. Statistical question
Which type of numerical data set can be counted in a finite matter? A. Categorical data B. Continuous data C. Discrete data D. NONE OF THE ABOVE
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The question “How old is my Mathematics teacher?” is an example of non- statistical question. Which of the following makes it as statistical question? A. How old is my teacher? B. What is the typical age of the grade 7 Mathematics teachers? C. How old is your Mathematics teacher? D. NONE OF THE ABOVE
Which of the following is an example of discrete data? A. Average daily temperature B. Number of Facebook likes C. Number of litters of milk in a gallon D. Volts of electricity
It is a used to determine changes in the attitude, characteristics and behavior of people by watching them. A. Interviews B. Focus Group Discussion C. Observation D. Survey Data
The following are examples of continuous data EXCEPT, A. Number of minutes to board the plane B. Number of votes in an election C. Water temperature D. Wind speed
What type of data is the time duration of a film? A. Categorical data B. Continuous data C. Discrete data D. All of the above
These are questions that requires the respondent to elaborate their points in a free form manner? A. Closed questions B. Open-ended questions C. Multiple – choice questions D. None of the above
Lesson
1
Real -Life Problems that can
be Solved by Statistics
Have you ever been an officer in your class? Let’s say you’ve been the class President. How were you determined as a class president? If an election was conducted, did they tally the results in order for you to know if you won or not? Let’s say you wanted to lead the entire student body and you want to be the SSG President. How many should vote for you to be declared as the SSG President? Is it different from the time you were voted as the class president?
A. Determine whether or not the question is a statistical question. 1. Who is my favorite Korean Drama star? 2. What are the favorite Korean Darma of the grade 7 students? 3. How many Covid-19 positive cases are there in Koronadal City? 4. What is the typical age of the grade 7 Mathematics teacher? 5. How many brothers and sisters does my classmates have?
B. Identify each of the following data sets as categorical (C) or numerical (N).
- Ages of grade 7 students
- Favourite flavour of ice cream for each of 6th graders
- Internet browsing hours spent of grade 7 students
- My favourite Milktea flavors
- Number of students in each section
What’s In
What’s New
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- Do students who spend more time in studying do better in exam? (Relationship question)
Example of Non-Statistical Questions:
- How old are you?
- What is your favorite subject?
- How many siblings does Elise have?
Take note that each example of non-statistical question above has definite answer and do not need data to be gathered.
Examples of Categorical Data
- Since our country is infected with Corona Virus, do you follow the health protocols given by the Department of Health?
- Wintermelon is my favorite milktea flavor.
- Blue signifies calmness, tranquility, relaxation and peace.
Examples of Numerical Data
A. Discrete Data 1. Number of boys and girls in grade 7 per section Sunflower 2. The result of rolling 3 dice 3. The number of books in the shelves
B. Continuous Data 1. The heights of all grade 7 students 2. Age of a persons 3. Distance travelled by an airplane overtime.
Sample problem:
On January 20, 2020, the first case of COVID-19 was reported in the Philippines.* This event was followed by the declaration of the COVID-19 outbreak as a global pandemic by the WHO on March 11, 2020.** To solve this problem, data are gathered to answer the following statistical questions.
- How many people on every province of the country are being infected by the virus, daily?
- What sectors of the society are severely affected by the pandemic?
- Among age groups of people in the country who are most vulnerable to be infected by the virus?
- How long do people recover from the virus?
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*WHO Philippines Corona Virus Disease (COVID-19) Situation Report 1 **National Library of Medicine – National Center for Biotechnology Information
Observe that the data needed to answer the statistical questions above have different nature. The number of people infected by the virus is a discrete data. The time it takes for people to recover from the virus is a continuous data. The sectors of the society that are severely affected by the pandemic & the people who are most vulnerable to be infected by the virus are categorical data.
How do you think gathering data to answer the statistical questions above can solve the problem on COVID-19 Pandemic? What other statistical questions and data are needed to address the problem.
A. Determine whether the question is a statistical question or not. 1. What time did I woke up this morning? 2. What are the heights of grade 7 Dalya students? 3. What were the high temperature of the regions in Mindanao yesterday? 4. How old am I? 5. Do students want face to face classes than online classes?
B. Identify whether the following if it is categorical, discrete or continuous data.
- The volume of a prism
- Hours of sleep of a high students
- The weight of a sack of rice
- The height of a pineapple plants
- Eye color of my pets
- Brand of the ball pens in a class
- The number of students in a class
- Number of languages spoken by Jose Rizal
- Lists of SSG officers
- The results of rolling two dices
What I Have Learned
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Lesson
2
Formulates Simple Statistical
Instruments
This lesson contains exciting activities in formulating simple statistical instrument. Good luck dear!
What’s In
####### Activity 1
Directions. Fill in the blank with the correct information.
Student Data
Name: _______________________________ Grade Level and Section: _____________ Age: ____ Sex: _____ Date of Birth: ____________ Place of Birth: _______________ Height (cm):_______ Weight (kg):________ Mother Tongue: _____________________ Address: ___________________________________________________________________ Mother’s Name: _____________________________ Occupation: __________________ Father’s Name: ______________________________ Occupation: __________________ Guardian’s Name: ___________________________ Occupation: __________________ Do you have any brothers and sisters? _____________ How many? ____________ Health Concerns: __________________________________________________________
Emergency Contacts: Name: ___________________________________ Phone Number: __________________ Address: __________________________________ Relationship: ___________________
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####### Activity 2
Your teacher wants to know more about you. The questions below were prepared. Kindly answer honestly the following questions.
- What are your hobbies? ________________________________________________
- What subject do you find the most difficult and Why? ____________________
- What do you do when you’re having a hard time in a subject?
- What achievement are you proudest of?
- How would you describe yourself?
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There are different statistical instruments that can be formulated and used to gather data depending on the needs. Listed below are some of the statistical instruments.
Observation- it focuses in determining the changes in the attitude, characteristics and behavior of people or other subjects. This technique includes watching and recording actions and behaviours.
Interviews- it is being performed through personally asking questions to people who have the authority or expertise to say something about the data needed.
The person gathering the data is called the interviewer, while the person supplying the data is the interviewee.
Focus Group Discussion (FGD) - it is used to know the thinking, feeling or opinion, about a certain phenomenon, idea and etc. FGD is conducted with a small group of people with common knowledge and common field (usually 6 to 8 people).
Questionnaire- if you have big number of sample, it is the most practical way to use. You gather data through writing. However, you must be careful presenting your questions, since we need to consider the culture, and characteristics of the respondents. You may use email, letter, or personally give your questionnaire to your respondents.
Using different questions, and approaches to questioning, can allow us access to the information we require. Questionnaires usually are comprised of a number of questions that can either be closed questions, open-ended questions, or multiple- choice.
Types of Questions
- Closed questions These are questions which can be answered with “Yes” or “No,” or they have a limited set of possible answers (such as: A, B, C, or All of the above). For example, ‘Do you wear glasses?’ the respondent either does (responding ‘yes’) or doesn’t (responding ‘no’) wear glasses.
What shows are you watching from 7: PM to 10:00 PM?
From 7:00 - 8:00 PM News TV; 9:00 - 10:00 PM Telenovela
What is It
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Open-ended questions These are questions that allow someone to give a free-form answer. Example, “How did you answer the modules?”
Multiple-choice questions These are questions that provide a certain number of specific response options as possible answers. An example of multiple-choice question would be:
“How do you spend your free time?”. a. reading c. surfing the internet
b. listening to radio d. watching TV e. others (please specify: __)
Survey – in a national level, surveys are usually covered by the government and other form of surveying organization such as National Statistics Office (NSO). A survey can also be done in small scale (i. a class of 25 students can be surveyed)
Examples of Forms Used as Statistics Instruments
Please fill in the blank with the correct information. 1. Name: __________________________________ 2. Age: _______________ 3. Birthday: ___________________________ 4. Height (cm): _____________ 5. Weight (kg): _____________ 6. The subject you spend most time studying in class: _______________ 7. The number of pets at home: __________ 8. The number of siblings in the family: ____________
Please encircle the letter that best applies to you. 9. The kind of book you prefer to read a. fiction c. mystery e. others (please specify) _____ b. novel d. comic 10. The way you travel to school a. by foot c. by bicycle e. others (please specify) _____ b. by car d. by bus
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You want to know the favorite subjects of your classmates. Formulate a sample questionnaire for this.
Examples of Interview Question
What are some of your academic strengths? What are your weaknesses? Why do you want to study here? What do you expect to be doing ten years from now? What subject in high school did you find most challenging?
What’s More
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What I Have Learned
Directions: Fill in the missing word in the blank. Choose the correct answer from the box.
- The most useful statistical instrument to be used with big number of respondents is _____________.
- _____________ is being carried out through personally asking questions to knowledgeable people about the data needed.
- The question “Do you prefer answering Self Learning Modules (SLMs) than workbooks?” is an example of ________________________.
- The changes in characteristics, behavior and _____________ of the people observed are the focus of observation.
- _____________ is a type of question that allows someone to give a free-form answer.
What I Can Do
Now, you will apply what you have learned about formulating statistical instrument. Use a separate answer sheet.
Directions as directed. 1. Identify a real-life problem that you are interested. 2. Form a statistical question about the problem you identified. 3. Formulate your own simple statistical instrument that can be used to answer your statistical question.
Great work! You did a good job in applying what you have learned.
Interview Closed Question Open-ended Question
Attitude Questionnaire Survey
MATH7 Q4 MOD1-1 - Module
Course: Applied Math (APMATH)
University: University of Santo Tomas–Legazpi
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