Republic of the Philippines
Department of Education
Regional Office IX, Zamboanga Peninsula
Z
est forP
rogressZ
eal ofP
artnership7
4 th QUARTER – Module 3
ORGANIZING DATA in a FREQUENCY DISTRIBUTION
Name of Learner: ___________________________
Grade & Section: ___________________________
Name of School: ___________________________
1 Mathematics – Grade 7
Alternative Delivery Mode
Quarter 4 - Module 3: Organizing Data in a Frequency Distribution 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 royalty.
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
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]
Development Team of the Module
Writer: Corazon M. Lutian
Editors: Salvador C. Bucoy, LMD
Shirley U. Yap
Layout Artist: Abdurauf J. Baldomero
Reviewers: EPS, Mathematics Vilma A. Brown, Ed. D.
Principal Reneboy F. Gutierrez
Management Team: SDS Roy C. Tuballa, EMD, JD, CESO VI ASDS Jay S. Montealto, CESO VI
ASDS Norma T. Francisco, DM, CESE
EPS Mathematics Vilma A. Brown, Ed. D.
EPS LRMS Aida F. Coyme, Ed. D.
2
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 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 was written as an alternative learning material for the lesson on Organizing Data in a Frequency Distribution for Mathematics 7- Fourth Quarter. It presents a step-by-step approach on how to organize statistical data in a frequency distribution supported by examples and exercises.
In this module, the learner is expected to:
⚫ organize data in a frequency distribution table. (M7SP-IVc-1) o define a frequency distribution
o identify the different columns in a frequency distribution o illustrate data in a frequency distribution
o organize data in a frequency distribution
What I Know
Directions: Read each statement carefully. Write the letter of the correct answer on your answer sheet.
1. It is an arrangement of data in tabular form.
A. illustrating data B. frequency C. frequency distribution D. organizing data
What I Need to Know
3
2. The following are parts of a frequency distribution EXCEPT.
A. tally marks B. range C. class interval D. frequency
3. The class size (c) is obtained by dividing the range by the ________.
A. highest score B. lowest score C. frequency D.
𝑘 = √𝑛
4. A group of students was tasked to determine the number of students who have Facebook, Twitter, or Instagram accounts in their class. What column in the frequency distribution table will the data collected be recorded?
A. class interval B. tally marks C. frequency table D. frequency 5. It refers to the difference between the highest score and the lowest score in an array.
A. range B. frequency C. class interval D. class size
[
What’s In
Directions: Consider the following blood types of twenty-five (25) regular blood donors to the Philippine National Red Cross (PNRC).
A, B, B, AB, O, O, O, B, AB, B, B, B, O, A, O, A, O, O, O, AB, AB, A, O, B, A
Fill out the table below:
BLOOD TYPE TALLY FREQUENCY
A ꟾꟾꟾꟾ
B ꟾꟾꟾꟾ - ꟾꟾ O ꟾꟾꟾꟾ - ꟾꟾꟾꟾ
AB ꟾꟾꟾꟾ
TOTAL 25
Guide Question:
How is the frequency column obtained?
Data which are organized in a table describe and analyze the given information more understandable and can even present a more logical interpretation.
What’s New
Directions: Set up a frequency table for the scores given and answer the guide questions that follow.
Situation: The following are the scores obtained by 15 students in a short test:
32, 30, 29, 29, 28, 28, 28, 27, 27, 27, 27, 26, 26, 25, 24
GUESS WHAT?
ACTIVITY
WHICH IS WHICH
ACTIVITY
4
SCORE (𝒙) TALLY FREQUENCY (f)
32 31 30 29 28 27 26 25 24
𝑛 = Guide Questions:
1. What does 𝑛 in the frequency column represent?
2. What score has the highest frequency?
3. What is the difference between the highest score and the lowest score?
4. What do you call the difference you obtained in number 3?
LESSON Organizing Data in a Frequency Distribution
What is It
There are many instances in the real world when a group of information have to be analyzed and interpreted. However, before this is done, devices such as tables have to be studied. These tables in Statistics are commonly referred to as Frequency Distribution Table or simply Frequency Distribution.
A frequency distribution is an arrangement of data that shows the frequency or occurrence of the different values in an experiment or study.
When beginning to analyze fewer data, it is convenient to organize them into an array – an arrangement of data from highest to lowest or vice-versa. However, there are cases when data are huge and numerous in number and that interpreting these data becomes so tiresome, and so a frequency distribution is to be constructed. Usually, constructing frequency distribution is advised for easier and faster analysis and interpretation of the gathered data when the number of observations (n) is 30 or more.
What is a frequency distribution?
A
Why construct a frequency distribution?
B
5
1. In constructing a frequency distribution with qualitative values, the following steps are considered.
a. Enumerate the categories or classifications and define these as your classes.
b. Count the number of observations falling under each category. These are the frequencies (f) of the different classes.
2. In constructing a frequency distribution with quantitative values, the following steps are suggested.
a. Determine the range (𝑟). Formula: 𝑟 = 𝐻𝑆 – 𝐿𝑆.
b. Solve for the number of classes or class intervals (𝑘) using the formula 𝑘 = √𝑛, where 𝑛 is the number of observations. Round off 𝑘 to the nearest whole number.
c. Determine the class size (𝑐) by dividing 𝑟 by 𝑘. Note 𝑐 must be the nearest number of decimal places as in the raw data.
d. Determine and enumerate the classes. Each class is an interval of values defined by its lower and its upper class limits. There must be enough classes to include the highest score and the lowest score. As a rule, the lowest value in the data becomes the lower class limit (LL) of the first class interval. Adding (𝑐) to the lower class limit of the preceding class interval obtains succeeding lower limits. The upper class limits (UL) are obtained using the formula:
𝑈𝐿 = 𝐿𝐿 + (𝑐) – 1
e. Count the number of observations falling in each class interval for the frequency (𝑓).
How to construct a frequency distribution?
C
SITUATION:
Below are the scores obtained by thirty-six (36) Grade 7-Students in a Mathematics Test.
25 30 17 34 18 46 11 39 29 52 48 35 23 16 37 51 13 8
16 31 43 44 16 31 9 19 27 45 14 22 23 32 29 16 32 10 SOLUTION:
Construct a frequency distribution using the data in the example.
STEP 1. Determine the range (𝑟). Formula: 𝑟 = 𝐻𝑆 – 𝐿𝑆.
𝑟 = 52 – 8 = 𝟒𝟒
STEP 2. Solve for the number of classes or class intervals (k) using the formula k = √𝑛 , where n is the number of observations.
(Note: number of classes or class intervals can be equal or more than 𝑘) 𝑘 = √36 = 𝟔
STEP 3. Determine the class size (𝑐) by dividing 𝑟 by 𝑘.
𝑐 = r 𝑘= 44
6 = 7.3 ≈ 𝟕
1. Since, 8 is the lowest score then the first class interval is 8 – 14.
STEP 4. Determine and enumerate the classes. Then count the number of students who got a score in each class interval.
EXAMPLE
6
The summary of data shown in the preceding table is called a frequency distribution.
Notice that the table presents the scores in groups called class interval in the first column. The tally marks in the second column records how often does each score appear and the number of occurrences is listed in the third column called the frequency (f).
What’s More
Directions: Study the situation below and answer the questions that follow.
The data below show the number of students living in the nearby barangays of the Don Pablo National High School.
BARANGAY NUMBER OF STUDENTS
Sta. Maria 1660
San Roque 600
Cabatangan 1 005
Tumaga 913
Canelar 806
1. What is the total number of students surveyed?
2. Which barangay has the highest frequency?
3. What barangay has the lowest number of students?
4. Determine the range of the data.
What I Have Learned
Directions: Below is a frequency distribution of the birth months of a G7 class with 50 students. Complete the table.
BIRTH MONTH TALLY MARKS) NO. OF STUDENTS (f)
1. January
‖
22. February
ꟾ
3. March
‖‖
4. April 4
5. May
‖‖ - ꟾ
Frequency Distribution of the Scores of 36 G7-Studens in a Mathematics Test
CLASS INTERVAL TALLY FREQUENCY
8-14 ‖‖ - ꟾ 6
15-21 ‖‖ - ‖ 7
22-28 ‖‖ 5
29-35 ‖‖ - ‖‖ 9
36-42 ‖ 2
43-49 ‖‖ 5
50-56 ‖ 2
𝒄 = 𝟕 𝒏 = 𝟑𝟔
FREQUENCY DISTRIBUTION TABLE
ACTIVITY 1
7
6. June 7
7. July 9
8. August 10
9. September
‖‖
10. October 1
11. November 0
12. December
ꟾ
1𝒏 =
Directions: Tabulate the following ages of thirty-five (35) elders housed in an Orphanage Facility in Zamboanga City into a frequency distribution using a class size of 5. Let the first interval begin with 60.
Ages of Elders in an Orphanage Facility in Zamboanga City
72 75 77 67 72 76 77 81 78 65 86 73 75 78 67 82 76 76 70 87 82 83 71 63 72 72 61 68 61 67 84 69 64 73 79
CLASS INTERVAL TALLY FREQUENCY
𝒄 = 𝒏 =
Guide Questions:
1. Determine the range of these data.
2. What title best describes the data in the frequency distribution?
3. What are the different columns in a simple frequency distribution?
What I Can Do
Directions: Using any available magazine or newspaper, cut a picture of data presented in a frequency distribution. Paste your picture on your answer sheet.
Directions: Collect the age profile of the members of at least five (5) families in neighborhood and then construct a frequency distribution for it. Present the raw data and the frequency distribution table on your answer sheet.
(Note: The parents / guardians may do the gathering of data.) ACTIVITY 2
ACTIVITY 1
ACTIVITY 2
8
Assessment
Directions: Choose the letter that corresponds to your answer.
1. Which of the following is NOT a part of a frequency distribution?
A. tally marks B. range C. class interval D. frequency
For items 2 to 5, consider the following scores in a 25-item test:
13, 15, 15, 16, 17, 19, 19, 20, 22, 22, 22, 25
2. What is the total number of scores (n)?
A. 𝑛 = 12 B. 𝑛 = 13 C. 𝑛 = 22 D. 𝑛 = 25
3. What is the range?
A. 𝑟 = 12 B. 𝑟 = 13 C. 𝑟 = 22 D. 𝑟 = 25
4. How many times does the score 19 occur?
A. 4 B. 3 C. 2 D. 1
5. What score has the highest frequency?
A. 12 B. 13 C. 22 D. 25
Directions: The following are the number of years in teaching of thirty (30) Mathematics teachers of a certain Junior High School in Zamboanga City.
1. Determine the range (𝑟).
2. What is the total number of observations (𝑛)?
3. Find 𝑘.
4. Solve for 𝑐.
5. Find the lower limit (LL) of the lowest class interval.
16, 7, 4, 15, 6, 15, 9, 9, 35, 16, 27, 32, 13, 7, 2, 23, 25, 14, 21, 16, 27, 5, 25, 12,
13, 18, 21, 23, 10, 2
ACTIVITY 1ACTIVITY 2
9
Answer Key
Wha t I Know :
1.C 2.
B 3.
D 4.
D 5.
A
Wha t’s In :
BL OO D
TY PE TA
LL Y FR EQ UE NC Y
ꟾꟾꟾꟾ AA 5
ꟾꟾꟾꟾ - B ꟾꟾ 7
ꟾꟾꟾꟾ - O ꟾꟾꟾ ꟾ 9
ꟾꟾꟾꟾ AB 4
TO TA L 25
Gu id e Q ue sti on A ns we r:
By c ou nti ng th e n umb er of blo od d on ors
un de r e ac h b lo od ty pe
Wha t’s N ew :
SC ORE ( 𝒙) TA LL Y FR EQU EN CY (f)
32
| 1
31 0
30
| 1
29
||
2
28
|||
3
27
|||
| 4
26
||
2
25
| 1
24
| 1
𝑛
=15
Guide Qu estio ns:
1.
n re pre sen ts th e t ota l n um be r o f st ud en ts
2.
27 3.
8 4.
ra ng e
Wha t I Have L ea rn ed :
BIRT H MO NTH TAL
LY MAR KS NO. OF
ST UDE NTS (f)
1.
Jan ua
‖ ry 2
2.
Fe bru ꟾ ary
1
3.
Ma
‖‖ rch 5
4.
Ap
‖‖ ril 4
5.
Ma
‖‖ - y ꟾ 6
6.
Jun
‖‖ - e ‖ 7
7.
‖‖ - July ‖‖
9
8.
Au gu
‖‖ st
‖‖
10
9.
Se pte mb
‖‖ er 4
10.
Octo be ꟾ r
1
11.
Nove mb er 0
12.
Dece mb ꟾ er
1
n = n = 5 0__
__
__
__
10
References:
Milagros. Pangan et. al, Statistics for College Students Makati: Grandwater Publications and Research Corporation, 1996.
Soledad J. Dilao et. al, Advanced Algebra, Trigonometry and Statistics Quezon City: SD Publications Inc., 2009.
Website:
“Presenting Numerical Data”, University of Leicester, Accessed August 22, 2020, https://www2.le.ac.uk/offices
/ld/all-resources/numerical-data/numerical-data
Wha t I Have Lea rn ed:
CL AS S I NT ER VA L TA
LL Y FR
EQ UE NC Y
60 – 64
‖‖
4
65 – 69
‖‖ - ꟾ 6
70 – 74
‖‖ - ‖ꟾ 8
75 – 79
‖‖ - ‖‖
10
80 – 84
‖‖
5
85 – 89 2 ‖
c = 5 n =
35
Gu id e Q ue sti on s:
1.
26 2.
Fre qu en cy D is tri bu tio n o f t he A ge s o f T hir ty -F iv e e ld ers h ou se d i n a n O rp ha na ge
F ac ilit y i n Z am bo an ga C ity
3.
Cla ss In te rv al, T ally M ark s a nd F re qu en cy .
Wha t I Ca n D o:
A ctiv ity 1
stud ent
’s an swer may vary th e se aso n.
Wha t I Ca n Do : A ctivity
2
stud ent
’s an swer may vary th e se aso n.
Ass ess men t:
A.
B.
1.
B 4.
C 1.
33 4 . 7
2.
A 5.
C 2.
30 5 . 2
3.
A 3.
5
11
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:
“I am a Filipino born to freedom, and I shall not rest until freedom shall have been added unto my inheritance—for myself and my children and my children’s children—
forever.”
