quarter 4 module 16: constructing a scatter...

Statistics and Probability

Quarter 4 – Module 16:

Constructing a Scatter Plot

Development Team of the Module

Writer: Rommel A. Paderagao

Editors: Nestor N. Sandoval, Josephine P. De Castro and

Pelagia L. Manalang

Reviewers: Josephine V. Cabulong, Rey Mark R. Queaño, Alfonso V. Mabuting and

Ermelo A. Escobinas

Illustrator: Jeewel L. Cabriga

Layout Artist: Ronnjemmele A. Rivera

Management Team: Wilfredo E. Cabral, Regional Director

Job S. Zape Jr., CLMD Chief

Elaine T. Balaogan, Regional ADM Coordinator

Fe M. Ong-ongowan, Regional Librarian

Aniano M. Ogayon, Schools Division Superintendent

Maylani L. Galicia, Assistant Schools Division Superintendent

Randy D. Punzalan, Assistant Schools Division Superintendent

Imelda C. Raymundo, CID Chief

Generosa F. Zubieta, EPS In-charge of LRMS

Pelagia L. Manalang, EPS

Statistics and Probability – Grade 11 Alternative Delivery Mode Quarter 4 – Module 16: Constructing a Scatter Plot First Edition, 2020 Republic Act 8293, Section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties.

Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio

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Office Address: Gate 2 Karangalan Village, Barangay San Isidro

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Telefax: 02-8682-5773/8684-4914/8647-7487

E-mail Address: [email protected]

Statistics and

Probability Quarter 4 – Module 16:

Constructing a Scatter Plot

ii

Introductory Message

For the facilitator:

Welcome to the Statistics and Probability for Senior High School Alternative

Delivery Mode (ADM) Module on Constructing a Scatter Plot!

This module was collaboratively designed, developed, and reviewed by educators

both from public and private institutions to assist you, the teacher or the

facilitator, in helping the learners meet the standards set by the K to 12

Curriculum while overcoming their personal, social, and economic constraints in

schooling.

This learning resource hopes to engage the learners into guided and independent

learning activities at their own pace and time. Furthermore, this also aims to help

learners acquire the needed 21st century skills while taking into consideration

their needs and circumstances.

In addition to the material in the main text, you will also see this box in the body of

the module:

As a facilitator, you are expected to orient the learners on how to use this module.

You also need to keep track of the learners' progress while allowing them to

manage their own learning. Furthermore, you are expected to encourage and assist

the learners as they do the tasks included in the module.

Notes to the Teacher

This contains helpful tips or strategies

that will help you in guiding the learners.

iii

For the learner:

Welcome to the Statistics and Probability for Senior High School Alternative

Delivery Mode (ADM) Module on Constructing a Scatter Plot!

The hand is one of the most symbolical parts of the human body. It is often used to

depict skill, action, and purpose. Through our hands we may learn, create, and

accomplish. Hence, the hand in this learning resource signifies that as a learner,

you are capable and empowered to successfully achieve the relevant competencies

and skills at your own pace and time. Your academic success lies in your own

hands!

This module was designed to provide you with fun and meaningful opportunities

for guided and independent learning at your own pace and time. You will be

enabled to process the contents of the learning resource while being an active

learner.

This module has the following parts and corresponding icons:

What I Need to Know

This will give you an idea of the skills or

competencies you are expected to learn in

the module.

What I Know

This part includes an activity that aims to

check what you already know about the

lesson to take. If you get all the answers

correct (100%), you may decide to skip this

module.

What’s In

This is a brief drill or review to help you link

the current lesson with the previous one.

What’s New

In this portion, the new lesson will be

introduced to you in various ways such as a

story, a song, a poem, a problem opener, an

activity, or a situation.

What is It

This section provides a brief discussion of

the lesson. This aims to help you discover

and understand new concepts and skills.

What’s More

This comprises activities for independent

practice to solidify your understanding and

skills of the topic. You may check the

answers to the exercises using the Answer

Key at the end of the module.

What I Have Learned

This includes questions or blank

sentences/paragraphs to be filled in to

process what you learned from the lesson.

What I Can Do

This section provides an activity which will

help you transfer your new knowledge or

iv

skill into real life situations or concerns.

Assessment

This is a task which aims to evaluate your

level of mastery in achieving the learning

competency.

Additional Activities

In this portion, another activity will be given

to you to enrich your knowledge or skill of

the lesson learned. This also aims for

retention of learned concepts.

Answer Key

This contains answers to all activities in the

module.

At the end of this module, you will also find:

The following are some reminders in using this module:

1. Use the module with care. Do not put unnecessary mark/s on any part of

the module. Use a separate sheet of paper in answering the exercises.

2. Don’t forget to answer What I Know before moving on to the other activities

included in the module.

3. Read the instruction carefully before doing each task.

4. Observe honesty and integrity in doing the tasks and checking your

answers.

5. Finish the task at hand before proceeding to the next.

6. Return this module to your teacher/facilitator once you are through with it.

If you encounter any difficulty in answering the tasks in this module, do not

hesitate to consult your teacher or facilitator. Always bear in mind that you are

not alone.

We hope that through this material, you will experience meaningful learning

and gain deep understanding of the relevant competencies. You can do it!

References This is a list of all sources used in

developing this module.

1

What I Need to Know

In the previous module, you were able to differentiate bivariate data from

univariate data as well as identify the variable/s that are present on given

situations. Illustrating the bivariate data and identifying the variables involved are

important especially in dealing with researches and studies that you will later

encounter on different fields. In this ADM module, we will specifically deal with

bivariate data and how presented variables are related as you construct a diagram

called “scatter plot”.

After going through this module, you are expected to:

1. illustrate a scatter plot; and

2. construct a scatter plot based on the given data.

Are you ready now to study how to construct a scatter plot using your ADM

module? Good luck and may you find it helpful.

2

What I Know

Directions: Choose the best answer to the given questions or statements. Write the

letter of your choice on a separate sheet of paper.

1. Which of the following is a graphical representation that shows how each

point collected from bivariate data are scattered on the Cartesian plane?

A. pictograph

B. scatter plot

C. bar graph

D. line graph

2. In constructing a scatter plot, which of the variables should be plotted

horizontally?

A. consistent variable

B. dependent variable

C. independent variable

D. depends on the given

3. Which geometric figure is used to show the relationship of the variables in a

scatter plot?

A. bar

B. comma

C. line

D. points/dots

4. The following are other names for a scatter plot EXCEPT:

A. xy plot

B. line graph

C. scatter grams

D. scatter diagram

5. Joana read an article from the Parenting.Firstcry.com that the height of the

offspring of a couple is inherited from their father. She surveyed the height

of her 10 classmates and their father to construct a scatter plot. Which

variable should be plotted on the x-axis?

A. height of their father

B. height of their mother

C. height of her classmates

D. annot be determined

3

6. In constructing a scatter plot, which of the variables should assume the

values of y-coordinate?




D. cannot be determined

7. According to Margaret Renkl of Women’s Health, the weight of an individual

is more likely inherited from his/her mother. If data of the weight of

individuals and their mothers are collected and a scatter plot is constructed,

which of the variables will assume the values of the abscissa?

A. no enough data

B. weight of the mother

C. weight of the father

D. weight of the individual

8. Which of the following chart can be used BEST to show the correlation

between two variables?

A. bar graph

B. line graph

C. pictograph

D. scatter plot

9. What do we consider in describing the relationship of the variables in a

scatter plot?

A. shape, trend, and variance

B. mean, mode, and median

C. form, trend, and variation

D. form, direction, and standard deviation

10. The trend of the points in a scatter plot suggests the ______ of the

correlation of the variables.

A. direction

B. shape

C. strength

D. variation

11. The closeness of the points around the line in a scatter plot suggests the

_________ of correlation of the variables.

A. form

B. mean

C. shape

D. variation and strength

4

12. If the points on a scatter plot follow a trend of a line, then there is _______

correlation between the variables involved.

A. curvilinear

B. form

C. linear

D. non-linear

13. Luffy finds out that the IQ score of a child is inherited from his/her mother.

What is the independent variable on the situation above?

A. IQ score

B. IQ score of the father

C. IQ score of the child

D. IQ score of the mother

14. Which of the following shows the scatter plot of the data below?

Order of period of the

subject 1 2 3 4 5 6 7 8

Grades 85 84 87 88 90 81 80 85

A. C.

B. D.

15. From number 14, what is the variable that will assume the values of x-coordinate?

A. average grade

B. grades C. order of the subject D. cannot be determined

5

Lesson

1 Constructing a Scatter Plot

From your previous knowledge on Mathematics, you learned to plot points in

a Cartesian plane or xy-plane.

Points in Cartesian plane are represented by an ordered pair (x,y). The

x-coordinate can be moved either left or right from 0 or origin. From where it ends,

the y-coordinate units will be moved either upward or downward and then mark

the point where the y-coordinate stopped.

Example: Plot point A with coordinates (2,3)

Step 1: Locate 2 on your x-axis.

Step 2: From 2 on x-axis, move the point upward since y-coordinate is

3.

Step 3: Mark the point where y-coordinate stops. That point is where

the x and y-coordinate met. Name point A.

6

Notes to the Teacher

Check the student’s level of readiness for the next topic. If

s/he did not answer most of the items and the guide questions,

you may provide another review activity about plotting of points

in a Cartesian plane.

What’s In

Where Am I Now?

Directions: Plot the following points in a Cartesian plane or xy-plane.

1. S (3, 2)

2. C (1, 4)

3. A (- 2, 3)

4. T ( -3,3)

5. E (- 2, -2)

6. R (2, -4)

7. P (2,2)

8. L (3, -1)

9. O (0,3)

7

What’s New

Directions: Refer to the Cartesian plane below. Determine the coordinate of the

points to decode the answer to the question given. Then, write the

name of the point to its corresponding coordinates.

Question: I am a graphical representation that shows the relationship of the

variables of bivariate data. What am I?

From the activity, what do you call the graph showing the relationship of the

variables of bivariate data?

8

What Is It

Scatter plot, scatter graph, scatter diagram, or scatter gram is a

graphical representation that shows the relationship or the correlation of two

variables of bivariate data.

Scatter plot shows how points collected from a set of bivariate data are

scattered on a Cartesian plane. It gives a good visual picture of how two variables

are related or associated with one another in terms of form, trend, and variation of

correlation. The form of points in the scatter plot determines the shape of the

correlation of the variables. The trend determines the direction of the points, either

the variables have positive, negative, or no correlation. The variation or strength of

correlation is based on the closeness of the points on a trend line and it determines

whether the variables have no, weak, moderate, strong, or perfect correlation.

In constructing a scatter plot, you should know how to plot points in a

Cartesian plane. The independent variable will assume the values of x or abscissa

while the dependent variable will assume the values of y or ordinate.

Example 1:

The given numbers are the age of a person in years and his/her

corresponding weight.

Age of a person (x)

11 12 13 14 15 16 17 18 19 20

Weight (y) 40 42 38 35 45 51 48 48 50 47

Since the weight of an individual depends on his/her age, the independent

variable is the age of the person which is plotted horizontally. The dependent

variable is the weight of the person, which is plotted vertically as shown in the

scatter plot below.

9

Example 2:

A Math teacher conducted a study regarding the performance of grade 11

students in General Mathematics. Their average grades were taken at different time

or period. The data are given below.

Order of period of the

subject 1 2 3 4 5 6 7 8

Average grades 86 88 84 82 82 81 80 79

From the data given, the independent variable is the order of the subject and

the dependent variable is the average grade. From this, order of the subject will be

plotted on the x-axis and grades will be plotted on the y-axis as illustrated below.

10

Example 3:

A researcher asked for the weight of 10 students together with the weight of

their mother (biological) and created a scatter plot as presented below.

Weight of mother 65 69 74 78 59 81 76 80 81 75

Weight of student 52 55 62 63 47 66 63 69 68 65

On the given, the independent variable is the weight of the mother while the

dependent variable is the weight of the student. The scatter plot is presented below.

11

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50

nu

mb

er o

f m

inu

tes

Age

What’s More

Activity 1.1: Construct the scatter plot of the following data by plotting the

points.

1. Sakura interviewed 9 of her classmates on their average daily allowance in peso

and their weight in kilogram. The results are given below. Construct a scatter

plot of the given data.

Daily allowance 35 55 60 65 45 55 70 70 77

Weight 40 38 45 43 60 41 63 57 60

2. A gym instructor believes that health should be maintained by anyone

regardless of age. That’s why he recorded the ages of his customers and the

number of minutes they spend in exercising. The data are as follows:

Age 16 18 20 24 26 30 45

Number of

minutes 50 65 70 35 45 60 70

3. A

12

0

10

20

30

40

50

60

0 20 40 60 80 100 120 140

____

____

____

____

____

__

______________________________

researcher interviewed 10 students about their height and the height of their

father. The results are as follows:

Height

of the father (x)

71 69 67 68 68 66 70 72 65 60

Height

of the

student (y)

71 69 69 65 66 63 68 70 60 58

Activity 1.2: Identify the variables (dependent or independent) on the given

situations. Then, construct the scatter plot.

1. Matalino High School is known for students who excel in Math. A researcher

recorded the IQ of the students and their scores on a 50- item Math test as the

focus of his study.

IQ scores 85 87 93 95 87 97 105 110 115 120

Test scores 21 23 30 34 31 35 40 42 45 48

0

10

20

30

40

50

60

70

80

58 60 62 64 66 68 70 72 74

Hei

ght

of

the

stu

den

t

Height of father

13

2. ABM 11 students believe on the value of thriftiness. That’s why they conducted

a research on selected elementary learners regarding the amount they save from their daily allowance and their corresponding weight as follows.

Amount saved in peso

10 8 15 20 5 3 5 25 10 15

Weight in kilogram 38 40 37 36 42 41 39 35 36 37

3. The data below are aptitude test scores (x) and scores in a long test in

Mathematics (y) of 15 students.

34

35

36

37

38

39

40

41

42

43

0 5 10 15 20 25 30

____

____

____

____

____

__

________________________

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40

____

____

____

____

____

____

_

_________________________

x 38 35 30 28 25 24 20 18 16 15 12 10 8 7 5

y 25 20 17 15 12 15 18 10 12 10 10 10 7 6 5

14

0

5

10

15

20

25

30

35

40

45

50

0 20 40 60 80 100 120 140

Sco

res

in M

ath

tes

t

No.of minutes spent in studying

76

77

78

79

80

81

82

83

84

85

86

87

0 20 40 60 80 100

Gra

des

Number of minutes spent in playing ML

Activity 1.3: Based on the scatter plot, determine the data and supply them

on the table below.

1.

Table:

Number of hours spent in studying (minutes)

Grades

2.

Table:

Number of

minutes spent in playing ML

Grades

15

0

5

10

15

20

25

30

35

40

0 50 100 150 200

Pri

ce o

f Lu

mp

ia

No.of produced Lumpia

3.

Table:

Number of produced

lumpia

Price of

lumpia

Activity 1.4

Directions: Construct the scatter plot based on the given data. Create the scatter

plot on a separate sheet of graphing paper.

1.

Age of COVID-19

recovered patients 26 28 32 36 40 43 45 22 50 54 34 65

Number of days they spent in the hospital 8 8 9 10 12 12 10 8 14 16 10 18

2.

Number of glasses of water drank by

students per day 10 8 12 11 15 7 12 13 9 7 5 12

Number of glasses of soft drinks

drank by students per day 2 4 2 1 0 4 2 3 4 5 4 2

16

What I Have Learned

Directions: Complete the following statements. Write the answers in your

notebook.

1. Scatter plot is used to show the relationship or _____________ of two

variables.

2. The __________ variable assumes the values of the x-coordinates.

3. The trend of the points in a scatter plot determines the __________ of the


4. The strength of the correlation of the variables is determined by the

_________ of the points on the trend line.

5. The dependent variable assumes the values plotted along the _______ -axis.

What I Can Do

Ask 15 of your classmates regarding their arm span and their height. Make a

scatter plot of the data collected on a separate sheet of paper. Your output will be

graded according to the rubrics below:

Neatness of the Output 10 points

Accuracy of the Scatter Plot 25 points

Presentation of Data 15 points

Total: 50 points

17

74

76

78

80

82

84

86

88

90

92

0 2 4 6 8 10 12

Assessment

Directions: Choose the best answer to the given questions or statements. Write the

letter of your choice on a separate sheet of paper.

1. It is a graphical representation that shows the correlation of two variables using

points or dots.

A. bar graph

B. line graph

C. pictograph

D. scatter plot

2. The direction of the points on a scatter plot determines the ______ of the


A. form B. strength

C. trend D. variation

3. Complete the statement:

The _______ variable is for the x-axis while the ________ variable is for the y-axis.

A. consistent, inconsistent B. independent, dependent

C. inconsistent, consistent D. dependent, independent

4. Which of the following tables corresponds to the scatter plot below?

18

A.

B.

C.

D.

5. Which of the following shows the scatter plot of the data below?

Order of period of the subject 1 2 3 4 5 6 7 8

Grades 85 84 87 88 90 81 80 85

A. C.

B. D.

6. In constructing a scatter plot, which of the variables should assume the values

of x-coordinate?





x 2 3 4 5 6 7 8 9 10

y 82 78 81 80 79 85 90 76 75

x 2 3 4 5 6 7 8 9 10

y 80 78 81 82 79 83 80 76 75

x 2 3 4 5 6 7 8 9 10

y 80 78 81 80 79 85 90 76 80

x 2 3 4 5 6 7 8 9 10

y 84 78 81 80 79 85 90 76 82

19

7. The direction of the points around the line in a scatter plot suggests the

_________ correlation of the variables.

A. form

B. shape

C. trend

D. variation/strength

8. According to a study, the height of an individual is more likely inherited from

his/her father. If data on the height of individuals and their fathers are collected

to construct a scatter plot, which of the variables will assume the plot as y-

coordinate?

A. height of the father

B. height of the individual

C. height of the mother


9. The form of the points in a scatter plot suggests the ______ of the correlation of

the variables whether linear or non-linear.

A. direction

B. shape

C. strength

D. variation

10. The relationship of the variables in a scatter plot is described in terms of its

______________.

A. shape, trend, and variance

B. mean, mode, and median

C. form, trend, and variation

D. form, direction, and standard deviation

11. Nami studied the results of the IQ test scores of children and the recorded IQ

scores of their parents. She noticed that the IQ of a child is more likely related

to the mother than that of the father. If a scatter plot will be constructed, what

is the independent variable on the situation above?

A. IQ score

B. IQ score of the father

C. IQ score of the child

D. IQ score of the mother

20

12. Which scatter plot is appropriate for the given data below?

x 14 13 17 16 13 15 16

y 160 154 164 162 158 165 170

A.

B.

C.

D.

21

13. Which of the tables contain the correct data based on the scatter plot below?

A.

x 1 2 3 4 5 6 7

y 92 90 87 90 92 91 88

B.

x 1 2 3 4 5 6 7

y 90 92 85 88 90 90 88

C.

x 1 2 3 4 5 6 7

y 90 92 87 88 91 90 88

D.

x 1 2 3 4 5 6 7

y 92 90 88 87 91 90 88

14. Choose the data that best complete the table based on the scatter plot below.

x 30 40 50 50 60 60 80

y

22

A.

y 90 92 88 90 87 90 88

B.

y 92 90 88 91 90 90 87

C.

y 91 92 90 88 92 90 88

D.

y 89 92 90 88 91 92 88

15. Mary Joy read from an article that the height of the offspring of a couple is

inherited from the father. She surveyed the height of her 10 classmates and

their fathers to construct a scatter plot. Which variable should be plotted on the

x-axis?

A. height of her classmates

B. height of their mothers

C. height of their fathers


23

Additional Activities

Form a group consisting of three (3) members. Conduct a survey involving

two variables with at least 15 respondents. Put the data in a table identifying the

independent and dependent variables, then construct a scatter plot. As part of your

advance study, determine the shape, trend, and variation of the variables involved.

Your output will be presented to the class and will be graded using the rubrics

below:

Organization of Data 10 points

Accuracy of the Scatter Plot 15 points

Presentation of the Output 15 points

Cooperation Among the Members 10 points

Total 50 points

24

Answer Key

What I Know

1.B

2.C

3.D

4.B

5.A

6.B

7.B

8.D

9.C

10.A

11.D

12.C

13.D

14.A

15.C

What’s In

What’s New

WHAT AM I?

The word to be formed is

“SCATTERPLOT”

What’s More

Activity 1.1

1.

2.

3.

25

Activity 1.2

1.

2.

3.

26

Activity 1.3

1.

No. of minutes

20

30

45

60

75

90

120

Grades

30

25

35

40

40

45

45

2.

No. of minutes Grades

20 86

25 84

30 85

35 83

40 80

50 85

60 81

65 82

70 78

75 80

80 81

85 77

90 79

3.

No. of lumpia

Price of lumpia

80 35

90 30

100 20

110 25

115 20

120 25

130 25

140 20

150 15

27

Assessment

1. D

2. C

3. B

4. A

5. A

6. C

7. C

8. B

9. B

10.C

11.D

12.B

13.C

14.A

15.C

What I have learned

1.correlation

2.independent

3.direction

4.variation

5.y-axis

Activity 1.4

1.

2.

Additional Activity

Students’ answer may vary.

28

References

Books

Albacea, Zita VJ., Mark John V. Ayaay, Isidoro P. David, and Imelda E. De Mesa.

Teaching Guide for Senior High School: Statistics and Probability. Quezon City: Commision on Higher Education, 2016.

Caraan, Avelino Jr S. Introduction to Statistics & Probability: Modular Approach.

Mandaluyong City: Jose Rizal University Press, 2011.

De Guzman, Danilo. Statistics and Probability. Quezon City: C & E Publishing Inc,

2017.

Punzalan, Joyce Raymond B. Senior High School Statistics and Probability.

Malaysia: Oxford Publishing, 2018.

Sirug, Winston S. Statistics and Probability for Senior High School CORE Subject A Comprehensive Approach K to 12 Curriculum Compliant. Manila: Mindshapers

Co., Inc., 2017.

Online Resources

Lane, David M. “Online Statistics Education: A Multimedia Course of Study.”

Accessed May 25, 2020. http://onlinestatbook.com/2/regression/intro.html

Quizizz. “Linear Regression | Algebra I Quiz” Accessed May 25, 2020.

https://quizizz.com/admin/quiz/5acae751c4daf70019c2369f/linear-

regression

Rourke, Emily O. “Performance Based Learning and Assessment Task Tuition Cost

Activity.” Accessed May 25, 2020. https://www.radford.edu/rumath-smpdc/Performance/src/Emily O’Rourke - Tuition Cost Activity.pdf

For inquiries or feedback, please write or call: Department of Education - Bureau of Learning Resources (DepEd-BLR)

Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600

Telefax: (632) 8634-1072; 8634-1054; 8631-4985

Email Address: [email protected] * [email protected]

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