4 th QUARTER Module 4: PROBLEMS ON QUARTILES AND DECILES FOR UNGROUPED DATA

Republic of the Philippines

Department of Education

Regional Office IX, Zamboanga Peninsula

Z

est for

P

rogress

Z

eal of

P

artnership

10

0

4

th

QUARTER – Module 4:

PROBLEMS ON QUARTILES AND

DECILES FOR UNGROUPED DATA

Name of Learner:

___________________________

Grade & Section:

___________________________

1

Mathematics – Grade 10 Alternative Delivery Mode

Quarter 4 - Module 4: Problems on Quartiles and Deciles for Ungrouped Data First Edition, 2020

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Published by the Department of Education Secretary: Leonor Magtolis Briones

Undersecretary: Diosdado M. San Antonio

Printed in the Philippines

Department of Education – Region IX, Zamboanga Peninsula Office Address: Tiguma, Airport Road, Pagadian City Telefax: (062) – 215 – 3751; 991 – 5975 E-mail Address: [email protected]

Introductory Message

Development Team of the Module

Writer: Glissette C. Gallo

Editors: Rosemary B. Garcia

Elizabeth M. Raciles, Ed.D.

Illustrator: Mildred P. Caceres

Layout Artist: Zandro G. Sepe, M.S.

Reviewers: EPS, Mathematics Vilma A. Brown, Ed.D.

Principal Zandro G. Sepe, M.S.

Management Team: SDS Roy C. Tuballa, EMD, JD, CESO VI

ASDS Jay S. Montealto, CESO VI

ASDS Norma T. Francisco, Ed.D.,CESE

EPS Mathematics Vilma A. Brown, Ed.D.

EPS LRMS Aida F. Coyme, Ed.D.

2

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 can 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. 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.

This module is designed for the learners to enhance their critical thinking and problem solving skills in dealing with word problems.

At the end of this lesson the learners are expected to:

• Solve word problems involving real - life situations on quartiles for ungrouped data • Solve word problems involving real - life situations on deciles for ungrouped data

What I Know

Directions: Choose the letter of the correct answer. Write your answer on a separate sheet.

1. What is the first step in solving problem involving quartile or decile?

A. Arrange the data entries from highest to lowest.

What I Need to Know

Problem: The following scores show the intelligence quotient (IQ) of 20

students of 10 - Apollo.

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B. Arrange the data entries from lowest to highest.

C. Arrange data entries in descending order.

D. Arrange data entries from largest to smallest.

2. Which of the following formula is used in solving for the position of quartile?

A.

𝑄

_𝑘

=

𝑘𝑁 4

B. 𝑄

𝑘

=

𝑘(𝑛+1) 10

C. 𝑄

𝑘

=

𝑘𝑁 10

D. 𝑄

𝑘

=

𝑘(𝑛+1) 4

3. What is the value of 𝑄

2

and 𝐷

5

?

A. 93

B. 95

C. 97

D. 98

4. Which of the following interpretations is NOT TRUE about 𝐷

₅

?

A. 75% of the students of 10 - Apollo has 97 or below IQ Score.

B. The median score of the data is 97.

C. The 5

th

_{decile of the data is 97.}

D. 50% of the students of 10 – Apollo has 97 or below IQ Score.

5. Which of the following is the CORRECT interpretation for 𝑄

₁

?

A. 50% of the students of 10 – Apollo has 91 or below IQ Score.

B. 25% of the students of 10 – Apollo has 97 or below IQ Score.

C. 25% of the students of 10 – Apollo has 92 or below IQ Score.

D.

50% of the students of 10 – Apollo has 97 or below IQ Score

.

What’s In

Directions: Choose the letter of the correct answer. Write your answer on a separate sheet.

1. What is the first step in solving for quartile or decile?

A. Arrange data in descending order.

B. Arrange the data in ascending order.

C. Arrange the data from the highest to the lowest.

D. Arrange the data from the largest to the smallest.

2. What is the formula in solving the quartile for ungrouped data?

A.

𝑄

_𝑘

=

𝑘(𝑛+1) 100

B. 𝑄

𝑘

=

𝑘(𝑛+1) 10

C. 𝑄

𝑘

=

𝑘𝑁 4

D. 𝑄

𝑘

=

𝑘(𝑛+1) 4

3. What is the value of 𝑄

3

?

A.

149

B. 153

C. 154

D. 157

4. What is the formula in solving the decile for ungrouped data? A. 𝐷𝑘= 𝑘(𝑛+1) 100 B. 𝐷𝑘 = 𝑘(𝑛+1) 10 C. 𝐷𝑘 = 𝑘𝑁 4 D. 𝐷𝑘 = 𝑘(𝑛+1) 4

Given the data:

134

137

142

144

147

147

4 5. What is the value of 𝐷3?

A. 144 B. 147 C. 149 D. 153

What’s New

Directions: Arrange the letters in the box to form a word and match it to its definition.

Write your answer on a separate sheet.

1. It is the 𝐷

₅

and 𝑄

₂

of the data.

2. It is a mathematical problem expressed entirely in words.

3. These are score points which divide a distribution into four equal parts.

4. These are score points which divide a distribution into ten equal parts.

5. It is a process in finding solution

.

What is It

LESSON

1

Problems on Quartiles and Deciles

for Ungrouped Data

These are the score points which divide a distribution into four equal parts.

Twenty-five percent (25%) of the distribution fall below the first quartile (Q

1

), fifty

percent (50%) fall below the second quartile (Q

2

), and seventy-five percent (75%) fall

below the third quartile (Q

3

).

The deciles are the nine score points which divide a distribution into ten equal

parts. The deciles are denoted as D

1

, D

2

, D

3

,…, D

9

. Ten percent (10%) of the

distribution fall below D

1

, twenty percent (20%) fall below D

2

, thirty percent (30%) fall

below D

3

, …,ninety percent (90%) fall below D

9

.They are computed in the same way

that the quartiles are calculated.

QUARTILES

A

DECILES

B

5

To solve for the position of the kth quartile and kth decile scores, follow the given formula below

EXAMPLE 1

In Rheem’s Coffee Shop, the owner is interested to know the amount of time it

takes the barista to prepare orders per customer. On a particular day, he asked his

store manager to record the service time of their barista for the first 15 costumers. The

data of the service time (to the nearest minute) are as follows: 6, 7, 8, 2, 4, 5, 7, 6, 9,

2, 9, 3, 11, 5, 10. What is the lower quartile of the service time recorded?

SOLUTION

STEPS

ILLUSTRATIVE EXAMPLE

STEP 1: Arrange the n data

entries from lowest to highest.

2, 2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11

*Note that based on the given data, n is 15 because

there are 15 values.

STEP 2: Find the position of the

lower quartile (

𝑄

₁

) using the

formula:

(Round off to the nearest integer if

necessary.)

𝑄

₁

=

𝑘(𝑛 + 1)

4

=

1(15 + 1)

4

=

16

4

= 4 ( 𝑤ℎ𝑖𝑐ℎ 𝑚𝑒𝑎𝑛𝑠 4𝑡ℎ 𝑑𝑎𝑡𝑎)

2, 2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11

Since Q

1

is the 4

th

data then Q

1

=

4. Therefore,

25% of the data distribution fall below 4.

EXAMPLE 2

The “Adopt a Student Program” of ZNHS is one of the laudable programs of

the school. The teacher sponsors are providing Php100 per week per recipient. Each

Quartiles

𝑄

_𝑘

=

𝑘(𝑛 + 1)

4

where:

n = total number of data

k = position of the quartile

Deciles

𝐷

_𝑘

=

𝑘(𝑛 + 1)

10

where:

n = total number of data

k = position of the decile

FORMULAS

Step 1: Arrange the n data entries from lowest to highest.

Step 2: Solve for the position of the quartile or decile using the correct

formula.

Step 3: Interpret the result.

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of the seventeen teachers in the program adopted 8, 1, 9, 2, 3, 5, 7, 1, 4, 6, 1, 3, 7, 6,

4, 4, and 5 students. Solve for the 5

th

_{decile (D}

5

) and interpret the result.

SOLUTION

STEPS

ILLUSTRATIVE EXAMPLE

STEP 1: Arrange the n data

entries from lowest to highest.

1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9

* Note that there are 17 data values (n) from the given data

STEP 2: Find the position of the

lower quartile using the formula:

(Round off to the nearest integer

if necessary.)

D

₅

=

k(n + 1)

10

=

5(17 + 1)

10

=

90

10

= 9 (𝑤ℎ𝑖𝑐ℎ 𝑚𝑒𝑎𝑛𝑠 𝑡ℎ𝑒 9𝑡ℎ 𝑑𝑎𝑡𝑎)

1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9

This means that 50% of the teacher

sponsors adopted 4 or less number of

students.

What’s More

ACTIVITY 1: CARDIOVASCULAR CONDITIONING

Directions: Perform as indicated. Write your answers on separate sheets.

Data: ____________________________________________________

Cardiovascular conditioning improves circulation and strengthens the heart, lungs

and blood vessels. It builds endurance and strength for the heart muscle.

Moreover, exercise conditions the heart to work more efficiently. Twenty (20)

aerobics practitioners recorded the average time (in minutes) of their individual

workout. The data are listed as follows:

70

72

68

73

43

40

45

40

74

54

80

50

82

50

65

35

62

30

30

55

a.) Arrange the given data from lowest to highest.

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UPPER QUARTILE

LOWER QUARTILE

Solution:

Solution:

Interpretation:

Interpretation:

ACTIVITY 2: TIME TO RECORD

Directions: Refer to the given data below. Solve for the decile scores and interpret

the results. Answer this activity on a separate sheet of paper.

Data: ________________________________________________

2

n

d

D

EC

IL

E

Solution:

Interpretation:

6

th

D

EC

IL

E

Solution:

Interpretation

8

th

D

EC

IL

E

Solution:

Interpretation

8

What I Have Learned

Directions. To check your understanding on this lesson, fill the table as indicated.

What I Can Do

Directions. Read the questions carefully. Write your answer on a separate sheet.

1. How do decile scores differ from quartile scores?

____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________

2. Are quartiles and deciles useful when applied in a real life situation?

____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ ____________________________________________________________

QUARTILE

Definition:

DECILE

Definition:

Formula:

Formula:

STEPS IN SOLVING WORD PROBLEM INVOLVING QUARTILE

AND DECILE

9

Assessment

Directions: Read carefully each item and encircle the corresponding letter of the

correct answer.

1. Find the first quartile for the following set of data 7, 9, 13, 4, 18, 3, 9, 10, 15, 8, 2,

6, 9.

A. 6

B. 9

C. 3.5

D. 4

2. A teacher gave a 50-point special test to 10 students. The scores were: 18, 36, 45,

40, 30, 38, 48, 27, 39, 25. If a student scored 25, in what quartile does it fall?

A. The score falls on the first quartile.

B. The score belongs to the second quartile

C. The score falls on the third quartile

D. The score is higher than the third quartile

For items 3-4 refer to the problem below.

3. What observation can you make about the ages of viewers?

A. Most of the viewers are of ages below 30.

B. Most of the viewers are teenagers.

C. Most of the viewers are adults.

D.

All of the above.

4. How many ages are above the third quartile?

A. There are 3 ages above the third quartile

B. There are 4 ages above the third quartile

C. There are 5 ages above the third quartile

D. There are 6 ages above the third quartile

5. The following data represent the number of biscuits in each student snack box: 6,

7, 9, 7, 8, 5,10, 7, 11. What interpretation can you draw using the following

positions: 𝑄

₁

=3

rd

_{, 𝑄}

2

=5

th

, 𝑄

3

= 8

th

?

A. 25% of the number of biscuits has a value ≤ 6.5

B. 50% of the number of biscuits has a value ≤ 7

C. 75% of the number of biscuits has a value ≤ 9.

D. All of the above

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For items 6-8, refer to the problem below:

6. What is the value of the 8

th

_decile?

A. 79

B. 82

C. 85

D. 87

7. What is the median of the scores of the 12 students who took the exam?

A. 77

B. 79

C. 82

D. 85

8. Alois got a score of 87 which is equivalent to the 8

th

_{decile. Which among the}

following is NOT true about his score?

A. He scored above 80% of his classmates.

B. 20% of his classmates got scores of 87 and above.

C. If the passing score is the upper quartile, he passed the exam.

D. His score is above the median score.

For items 9-10, refer to the problem below:

9. What is the value of the 4

th

_decile?

A. 330

B. 380

C. 420

D.430

10. Which of the following interpretation is correct?

A. 50% of the prices are less than or equal to Php 550.

B. 70% of the prices are greater than or equal to Php 550.

C. 30% of the prices are less than or equal to Php 550.

D. 10% of the prices are greater than or equal to Php 550.

Additional Activities

Directions: Refer to the given problem below and answer the questions that follow

.

Write the answers on separate sheets.

Questions:

1. List the data that are below 𝑄

₁

.

Answer: _____________________________

Mr. Sebastian conducted an exam to 12 students in his Geometry class. The

following were the test scores of his students: 56, 62, 65, 70, 73, 77, 79, 82,

85, 87, 92 and 99.

A survey of 12 randomly selected tax returns as to the number of claimed

dependents yielded the following: 1, 4, 5, 6, 1, 3, 3, 2, 5, 6, 4, 3.

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2. List the data that are below 𝐷

₇

.

Answer: ____________________________

3. List the data that are above 𝐷

₂

.

Answer:_____________________________

4. Solve for the third quartile and interpret.

Answer:_____________________________

5. Solve for the 4

th

_{decile and interpret.}

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References:

15

I AM A FILIPINO

by Carlos P. Romulo

I am a Filipino – inheritor of a glorious past, hostage to the uncertain future. As such, I must prove equal to a two-fold task – the task of meeting my responsibility to the past, and the task of performing my obligation to the future.

I am sprung from a hardy race – child many generations removed of ancient Malayan pioneers. Across the centuries, the memory comes rushing back to me: of brown-skinned men putting out to sea in ships that were as frail as their hearts were stout. Over the sea I see them come, borne upon the billowing wave and the whistling wind, carried upon the mighty swell of hope – hope in the free abundance of the new land that was to be their home and their children’s forever. This is the land they sought and found. Every inch of shore that their eyes first set upon, every hill and mountain that beckoned to them with a green and purple invitation, every mile of rolling plain that their view encompassed, every river and lake that promised a plentiful living and the fruitfulness of commerce, is a hollowed spot to me.

By the strength of their hearts and hands, by every right of law, human and divine, this land and all the appurtenances thereof – the black and fertile soil, the seas and lakes and rivers teeming with fish, the forests with their inexhaustible wealth in wild and timber, the mountains with their bowels swollen with minerals – the whole of this rich and happy land has been for centuries without number, the land of my fathers. This land I received in trust from them, and in trust will pass it to my children, and so on until the world is no more.

I am a Filipino. In my blood runs the immortal seed of heroes – seed that flowered down the centuries in deeds of courage and defiance. In my veins yet pulses the same hot blood that sent Lapulapu to battle against the alien foe, that drove Diego Silang and Dagohoy into rebellion against the foreign oppressor.

That seed is immortal. It is the self-same seed that flowered in the heart of Jose Rizal that morning in Bagumbayan when a volley of shots put an end to all that was mortal of him and made his spirit deathless forever; the same that flowered in the hearts of Bonifacio in Balintawak, of Gregorio del Pilar at Tirad Pass, of Antonio Luna at Calumpit, that bloomed in flowers of frustration in the sad heart of Emilio Aguinaldo at Palanan, and yet burst forth royally again in the proud heart of Manuel L. Quezon when he stood at last on the threshold of ancient Malacanang Palace, in the symbolic act of possession and racial vindication. The seed I bear within me is an immortal seed.

It is the mark of my manhood, the symbol of my dignity as a human being. Like the seeds that were once buried in the tomb of Tutankhamen many thousands of years ago, it shall grow and flower and bear fruit again. It is the insigne of my race, and my generation is but a stage in the unending search of my people for freedom and happiness.

I am a Filipino, child of the marriage of the East and the West. The East, with its languor and mysticism, its passivity and endurance, was my mother, and my sire was the West that came thundering across the seas with the Cross and Sword and the Machine. I am of the East, an eager participant in its struggles for liberation from the imperialist yoke. But I know also that the East must awake from its centuried sleep, shake off the lethargy that has bound its limbs, and start moving where destiny awaits.

For I, too, am of the West, and the vigorous peoples of the West have destroyed forever the peace and quiet that once were ours. I can no longer live, a being apart from those whose world now trembles to the roar of bomb and cannon shot. For no man and no nation is an island, but a part of the main, and there is no longer any East and West – only individuals and nations making those momentous choices that are the hinges upon which history revolves. At the vanguard of progress in this part of the world I stand – a forlorn figure in the eyes of some, but not one defeated and lost. For through the thick, interlacing branches of habit and custom above me I have seen the light of the sun, and I know that it is good. I have seen the light of justice and equality and freedom, my heart has been lifted by the vision of democracy, and I shall not rest until my land and my people shall have been blessed by these, beyond the power of any man or nation to subvert or destroy.

I am a Filipino, and this is my inheritance. What pledge shall I give that I may prove worthy of my inheritance? I shall give the pledge that has come ringing down the corridors of the centuries, and it shall be compounded of the joyous cries of my Malayan forebears when first they saw the contours of this land loom before their eyes, of the battle cries that have resounded in every field of combat from Mactan to Tirad Pass, of the voices of my people when they sing: