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Mathematics
Quarter 4 - Module 2:
Gathering Statistical Data
Mathematics - Grade 7
Alternative Delivery Mode
Quarter 4 - Module 2: Gathering Statistical Data
First Edition, 2020

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 What I Need to Know

This module is designed and written with you in mind. It is here to help you master on
how to gather the statistical data. The scope of this module permits it to be used in many ways.
The language recognizes the diverse vocabulary level of students. The lessons are arranged to
follow the standard sequence of the course. But the order in which you read them can be changed
to correspond with the textbook you are now using.
After going through this module, you are expected to: gather statistical data.

What I Know

Direction: Choose the letter of the best answer. Write your chosen letter on a separate sheet of
paper.

1. It is the set of all persons, animals, or objects involved in a statistical study where data
are collected.
A. population C. parameters
B. sample D. Statistics

2. This kind of data is the measure or amount represented by numbers.

A. qualitative data C. quantitative data
B. primary data D. secondary data

3. This is known as “area” sampling.

A. stratified random sampling C. cluster sampling
B. simple random sampling D. systematic random sampling

4. Population is first divided into subsets based on homogeneity.

A. stratified random sampling C. cluster sampling
B. simple random sampling D. systematic random sampling

5. Which of the following is an example of a population?

A. age of all members of the family
B. marital status of 50% selected from a large city
C. weights of 100 packages in LBC
D. yield of tomatoes per acre for 10 pieces in land

6. Which of the following is an example of a sample?

A. the total number of people infected by the COVID-19 in the Philippines
B. all students at Fort Bonifacio High School
C. the overall number of voters in the Philippines
D. Grade 7 students at Fort Bonifacio High School

7. A survey will be given to 100 students randomly selected from the freshmen class at Fort
Bonifacio High School. What is the population?
A. the 100 selected students
B. all freshmen at Fort Bonifacio High School
C. all students at Fort Bonifacio High School
D. all of the above

8. Fifty bottles of water were randomly selected from a large collection of bottles in a
company's warehouse. These fifty bottles are referred to as the _________.
A. population C. parameters
B. sample D. Statistics

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 Lesson
Gathering Statistical Data
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Sometimes, when you try to describe sets of data, you say it is too small or too large. The
data to be gathered depend upon the purpose they are to serve.

The word “population” refers to the groups or

aggregates of people, objective, material, events, or
things of any form. Sometimes populations can be
very large. In order to save time and money,
statisticians may study only a part of the
population called a “sample.” It is a subgroup of
population.
Samples are taken from the population so as to
represent the population’s characteristics or traits.
The measures of the population are called
“parameters”, while those of the samples are
called “estimates” or “statistics”.

What’s In
Activity 1: MY QUESTIONNAIRE!
Directions: A questionnaire is a statistical device or an
instrument that is made up of a series of questions that
are close-ended or open-ended. It was developed in
1838 by the Statistical Society of London. Create one
example of a closed – ended and an open – ended format
of questionnaire with two questions each.

https://www.questionpro.com/blog/what-is-a-questionnaire/

What’s New

Activity 2: TARGET TASK!

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Directions: Angelo wants to know how many games a teenager in the Philippines have on their
mobile phones.

1. What is the population for Angelo’s

question?
2. Explain why gathering data for this
population would be difficult.
3. Give an example of a sample that Angelo
could use to help him answer his question.

https://creazilla.com/nodes/25700-red-push-pin-clipart

What is It
Considering all the members of a population to be the subject of a
statistical study can be quite challenging. It can be costly and time
consuming. Thus, the researcher must take a sample from the population
using some techniques. In a statistical study, SAMPLING TECHNIQUE
refers to how we select members from the population to be in the
study. If a sample is not randomly selected, it will probably be biased in
some way and the data may not be the representative of the population.
Sampling techniques can be classified as probability sampling and
nonprobability sampling.

Probability Sampling
Probability sampling means that every member of the population has a chance of being
selected. It is mainly used in quantitative research. If you want to produce results that are
representative of the whole population, probability sampling techniques are the most valid
choice.

There are four main types of probability sampling.

SIMPLE RANDOM SAMPLING

Every member of the population has an equal chance of
being selected. Your sampling frame should include the
whole population. To conduct this type of sampling, you
can use tools like random number generators or other
techniques that are based entirely on chance.

Example:
You want to select a simple random sample of 100 employees of Company X. You assign
a number to every employee in the company database from 1 to 1000 and use a random
number generator to select 100 numbers.

SYSTEMATIC SAMPLING
It is similar to simple random sampling, but it is usually
slightly easier to conduct. Every member of the
population is listed with a number, but instead of
randomly generating numbers, individuals are chosen
at regular intervals.

Example:
All employees of the company are listed in alphabetical order. From the first 10
numbers, you randomly select a starting point: number 6. From number 6 onwards,
every 10th person on the list is selected (6, 16, 26, 36, and so on), and you end up with
a sample of 100 people.
If you use this technique, it is important to make sure that there is no hidden pattern in
the list that might skew the sample. For example, if the HR database groups employees by
team, and team members are listed in order of seniority, there is a risk that your interval
might skip over people in junior roles, resulting in a sample that is skewed towards senior
employees.

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 STRATIFIED RANDOM SAMPLING
This involves dividing the population into
subpopulations that may differ in important ways. It
allows you to draw more precise conclusions by
ensuring that every subgroup is properly represented in
the sample.

To use this sampling method, you divide the population into subgroups (called strata)
based on the relevant characteristic (e.g., gender, age range, income bracket, job role).

Based on the overall proportions of the population, you calculate how many people should
be sampled from each subgroup. Then, you use random or systematic sampling to select
a sample from each subgroup.
Example:
The company has 800 female employees and 200 male employees. You want to ensure
that the sample reflects the gender balance of the company, so you sort the population
into two strata based on gender. Then, you use random sampling on each group,
selecting 80 women and 20 men, which gives you a representative sample of 100 people.

CLUSTER SAMPLING
This also involves dividing the population into
subgroups, but each subgroup should have similar
characteristics to the whole sample. Instead of
sampling individuals from each subgroup, you
randomly select entire subgroups.

Cluster sampling is sometimes referred to as an “area sampling” because it is frequently

applied on a geographical basis. If it is practically possible, you might include every
individual from each sampled cluster. If the clusters themselves are large, you can also
sample individuals from within each cluster using one of the techniques above.

This method is good for dealing with large and dispersed populations, but there is more
risk of error in the sample, as there could be substantial differences between clusters. It
is difficult to guarantee that the sampled clusters are really representatives of the whole
population.

Example:
In a large school district, all teachers from two buildings are interviewed to determine
whether they believe the students have less homework to do now in a midst of pandemic
than last year.

Nonprobability Sampling
In this sampling technique, individuals are selected based on non-random criteria, and
not every individual has a chance of being included.

This type of sample is easier and cheaper to access, but it has a higher risk of sampling
bias. That means, the inferences you can make about the population are weaker than with
probability samples, and your conclusions may be more limited. If you use a non-probability
sample, you should still aim to make it as representative of the
population as possible.

There are four main types of nonprobability sampling.

PURPOSIVE SAMPLING
The sample is selected based on the objective or
purpose of the study.
Example:
You want to know more about the opinions and experiences of disabled students
at your school, so you purposefully select a number of students with different
support needs in order to gather a varied range of data on their experiences with
student services.

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 CONVENIENCE SAMPLING
In this sampling technique, samples are chosen
because of their availability. This is the easiest way
of getting respondents.

Example:
You are researching opinions about student support services in your school, so
after each of your classes, you ask your fellow students to complete a survey on
the topic. This is a convenient way to gather data, but as you only surveyed
students taking the same classes as you at the same level, the sample is not
representative of all the students at your school.

QUOTA SAMPLING
It is the process of selecting a sample based on the
specified number of members needed in the study.

Example:
A researcher wants to survey individuals about what smartphone brand they prefer
to use. He/she considers a sample size of 500 respondents. Also, he/she is only
interested in surveying ten states in the Philippines.

SNOWBALL SAMPLING
This is also known as referral sampling, wherein the
researcher asks referrals from the participants to
locate potential members of the sample who are hard
to find.

Example:
You are researching experiences of homelessness in your city. Since there is no list
of all homeless people in the city, probability sampling is not possible. You meet
one person who agrees to participate in the research, and she puts you in contact
with other homeless people that she knows in the area.

Even before birth, our brains collect data. In the womb, babies store
information on the prosody of their mother’s voice (intonation, rhythm, and
verbal stress). Then, as newborns, they differentiate and prefer her voice
rather than other female’s voice. DATA COLLECTION is a systematic
process of gathering observations or measurements. Whether you are
performing research for business, governmental, or academic purposes,
data collection allows you to gain first-hand knowledge and original insights
into your research problem.

There is not one “best” data collection technique — every process comes with the pros and cons.
Some methods are better for projects that only require quantitative data, while others are better
for uncovering qualitative data.

DATA
QUANTITATIVE QUALITATIVE
- Numerical data (two types) - Descriptive data (based on
- Discrete (Counting) observations)
- Continuous (Measurement) - Involves 5 senses
- See, feel, taste, hear, and smell

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The following are some methods of collecting data:

METHOD WHEN TO USE HOW TO COLLECT DATA

Observation It is used to understand Measure or survey a sample without trying to
something in its natural affect them.
setting.
Interview/ It is used to gain an in- Verbally ask participants open-ended
focus group depth understanding of questions in individual interviews or focus
perceptions or opinions on group discussions.
a topic.

Questionnaire/ It is used to understand the Distribute a list of questions to a sample

Survey general characteristics or online, in person, or over-the-phone.
opinions of a group of
people.

Secondary data It is used to analyze data Find existing datasets that have already been
collection from populations that you collected from sources such as government
can’t access first-hand. agencies or research organizations

What’s More
Activity 3: SKILL BOOSTER 101
A. Directions: On the blank before each item, write P if the given example describes a
population or S if it describes a sample.
_____ 1. All students who joined from each _____ 4. The entire harvest of corn in a farm
contest
_____ 2. Five representatives from each _____ 5. A pinch of salt from a jar
section
_____ 3. A part of the whole cake _____ 6. Three colors in a rainbow

B. Directions: Identify whether the following items are quantitative or qualitative data. Write
QUANTI for quantitative data and QUALI for qualitative data on the blanks provided.

________ 1) Civil status ________ 4) Number of Siblings

________ 2) Nationality ________ 5) Speed of light
Minimum salary of
________ 3) Body Mass Index ________ 6)
employee

C. Directions: Identify the sampling technique used in each item. Choose the letter of your
choice below.

A. Random Sampling D. Cluster Sampling

B. Stratified Sampling E. Convenience Sampling

C. Systematic Sampling F. Snowball Sampling

________ 1) The owner of the store writes all the names of the members of his staff in
pieces of paper, and then draws 15 members who will be part of the survey.
________ 2) A marketing staff member is conducting a survey and asks every 20 th
customer leaving the store.
________ 3) A marketing staff member is conducting a survey and asks 100 customers
who are leaving the store.
________ 4) A marketing staff member is conducting a survey and asks 10 customers in
each branch of the store.

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 ________ 5) A marketing staff member is conducting a survey and asks customers
coming from the stores in Metro Manila only.

What I Have Learned

POPULATION SAMPLE SIMPLE RANDOM
- refers to the groups
SAMPLING
- subgroup of
or aggregates of population -every member of the
people, objective, population has an equal
material, events, or CLUSTER chance of being selected.
things of any form.
SAMPLING STRATIFIED
SYSTEMATIC - dividing the population RANDOM
into subgroups, but each
RANDOM subgroup should have - you divide the population
similar characteristics to into subgroups (called
- individuals are chosen
the whole sample. strata) based on the
at regular intervals. relevant characteristic

PURPOSIVE CONVENIENCE
QUOTA SAMPLING
SAMPLING SAMPLING
- the sample is selected - samples are taken - there is a specified
based on the objective or because of its number of members
purpose of the study. availability. needed in the study.

SNOWBALL QUALITATIVE QUANTITATIVE

SAMPLING DATA DATA
- researchers ask for referrals - representations of a - it is a measure or
from the participants to
locate potential members of
class such as words amount represented by
the sample. or symbols. numbers.

What I Can Do
Activity 4: I AM A RESEARCHER!
Directions: You are working as a researcher in the Philippine
Statistics Office. As part of your work, you are tasked to get
information about a certain family (can be your neighborhood
etc.). Ask the permission of a family head in your barangay
to allow you to get the information about his or her family.
Record and analyze the data you get by generalization.
Write a reflective essay regarding your experiences while
doing this task. Use the guided questions below. You may
scan the QR Code to see the rubric.
Guided Questions:
1) What steps did you take in constructing the questionnaire?
2) Was it easy to gather data? Why?
3) What are the things you have learned in doing the project?
4) Did you find this lesson significant to your future career? How?

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 Assessment

A. Direction: Choose the letter of the best answer. Write your chosen letter on a separate sheet
of paper.

1. Fifty bottles of water were randomly selected from a large collection of bottles in a
company's warehouse. These fifty bottles are referred to as the ______________.
A. population C. parameters
B. sample D. Statistics

2. Fifty bottles of water were randomly selected from a large collection of bottles in a
company's warehouse. The large collection of bottles is referred to as the __________.
A. population C. parameters
B. sample D. Statistics

3. It is a branch of Mathematics that deals with the study of defining a problem, and
collecting, organizing, analyzing, and interpreting data for the purpose of making a
conclusion.
A. Geometry C. Statistics
B. Sample D. Trigonometry

4. Which of the following data is NOT AN EXAMPLE of qualitative data?

A. color C. jeepney fare
B. gender D. relationship status

5. Which of the following best illustrates a population?

A. all the students in the school
B. average monthly salary of 10 families
C. eight players in a basketball team
D. fifteen students as Grade 7 representatives

6. What sampling technique is being illustrated by the statement: the store manager selects
every 5th customer who enters the store for a survey?
A. random C. stratefied
B. systematic D. cluster

7. What sampling technique is being illustrated by the statement: In a large sports arena,
all spectators from two buildings are interviewed to determine whether they believe
basketball players have more shooting practices to do now than in previous years.
A. random C. stratefied
B. systematic D. cluster

8. What sampling technique is being illustrated by the statement: A student council surveys
100 students by getting random samples of 25 freshmen, 25 sophomores, 25 juniors, and
25 seniors.
A. random C. stratefied
B. systematic D. cluster

9. A friend recommended a possible respondent in your study. What kind of sampling

technique was done?
A. purposive C. snowball
B. convenience D. quota

10. Which of the following is an example of an indirect method of collecting data?

A. observation C. conversation
B. interview D. questionnaire

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