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Mathematics
Quarter 4 – Module 3
Organizing Data in the Frequency
Distribution Table
Mathematics – Grade 7
Alternative Delivery Mode
Quarter 4 – Module 3 – Organizing Data in the Frequency Distribution Table
First Edition, 2021

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Published by the Department of Education

Secretary : Leonor Magtolis Briones
Undersecretary : Diosdado M. San Antonio

Development Team of the Module

Writer/Illustrator/Layout Artist/Editor:
Salvador P. Yanga Jr.
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Evangeline G. Pangan

Content Evaluator : Lhio Roem R. Dela Cruz

Language Evaluator: Ma. Vilma L. Adonis
Layout Evaluator : Cynthia V. Aguinaldo
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Gregorio C. Quinto, Jr.
Rainelda M. Blanco
Agnes R. Bernardo
Francisco B. Macale
Glenda S. Constantino
Joannarie C. Garci

Department of Education--- Schools Division of Bulacan

Office Address: Curriculum Implementation Division

Learning Resource Management and Development System (LRMDS)
Capitol Compound, Guinhawa St., City of Malolos, Bulacan
E-mail address: lrmdsbulacan@deped.go
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Mathematics
Quarter 4 – Module 3
Organizing Data in the Frequency
Distribution Table
Introductory Message

This Self-Learning Module (SLM) is prepared so that you, 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 Teachers 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 exercise 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.

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 This module provides different activities that will assist you to learn about data
.
organization and how to create and complete a frequency distribution table.

At the end of this module, you are expected to:

• define and describe a frequency distribution table and
• determine the parts and be able to read and complete a frequency
distribution table.

Direction: Multiple Choice. Write the letter of the correct answer on the space provided for
before each number.

________ 1. What do you call the difference between the highest value minus the lowest value
in a distribution?
a. mean b. range
c. class interval d. class boundary

________ 2. What is the number that corresponds to the tally of the occurrence of a value
inside a class interval?
a. class size b. class mark
c. class interval d. frequency

________ 3. It refers to the magnitude of the class interval.

a. class interval b. class boundary
c. class size d. lower limit

________ 4. The Frequency Distribution Table has what type of data?

a. grouped data b. ungrouped data
c. actual values d. graded values

________ 5. The class interval contains limits – which of the of these determine the smallest
possible value?
a. class mark b. lower limit
c. upper limit d. class boundary

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________ 6. In a distribution of 50 people the range is 121, if asked to make 10 class intervals,
what would be the appropriate class size?
a. 5 b. 10
c. 12 d. 8

________ 7. The number of respondents in a collection of data sets corresponds to the total
sum of _________.
a. frequencies b. scores
c. ranks d. intervals

________ 8. In a distribution table the presentation of data is always in what form?

a. graph b. illustrative
c. tabular d. textual

Refer to the table below for items 9-15

Class Interval Frequency Class Mark <CF
11 – 15 2 13 2
16 – 20 4 18 6
21 – 25 12 23 18
26 – 30 15 28 33
31 – 35 4 33 38
36 – 40 3 38 40

__________ 9. What class interval has the highest frequency?

a. 11 – 15 b. 16 – 20
c. 26 – 30 d. 36 – 40

__________ 10. What class interval has the lowest frequency?

a. 11 – 15 b. 16 – 20
c. 26 – 30 d. 36 – 40

__________ 11. How many respondents were in the distribution?

a. 10 b, 20
c. 25 d. 40

__________ 12. Where can you find the highest possible score?
a. first interval b. second interval
c. middle interval d. last interval

__________ 13. What is the class size for each class interval?
a. 3 b, 5
c. 6 d. 4

__________ 14. What is the < cumulative frequency of the last interval?
a. 33 b, 38
c. 40 d. 18

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__________ 15. What is the lower limit for the second class interval?
a. 21 b, 16
c. 35 d. 40

One of the essential factors to remember in presenting and organizing data is

considering the accuracy and verification of numerical values. Suppose that you are assigned
to keep a record of attendance for your class. Kindly answer the following questions.

What are the first things that you would likely want to
have?

What is the first set of data that you think is the most
important?

How can you make sure that your records are correct
and updated?

The Municipal Civil Registry in your town generates and organizes different kinds of
data from number of births, weddings, occasions and donations to income taxes, tax refunds
and the municipal logistics. These types of data are numerical in nature and can help us
citizens as well as government officials in making informed decisions.

You might not be keenly aware of it but we can see charts and frequency tables almost
on a daily basis. Line graphs, bar graphs and pie graphs are made mostly coming from
frequency tables and tabulated data – understanding how that works gives us better insights
than most people who don’t know how to read tables and graphs. This lesson may also serve
as a perquisite for further statistical topics for later studies.

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 The use of the Frequency Distribution Table is a necessary tool and as a student you
should be able to do your part in understanding how this table works and how it increases
your chances of being well-informed and knowledgeable.

Remember that in presenting data, we try to be as accurate and as efficient as possible

to minimize work and errors. In the event when we are trying to present a set of values, the
size of the data or the number of scores becomes somewhat problematic when a sample
exceeds 30 or more values. To remedy this situation, we can use the tabular form or the
frequency distribution table.

Example for this is the set of data below.

9 11 12 14 15

15 16 17 19 20

20 20 22 26 28

29 30 30 30 30

31 33 35 37 40

43 45 46 47 48

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 The first thing to consider in making a Frequency Distribution Table is the class size.
To do this, start by finding the range. The range is defined as the difference between the
highest score and the lowest score.

RANGE = Highest Value – Lowest Value

Range = HV – LV

To determine the class size you have to decide how many class intervals you need to
present and it should be between 6 to 12 intervals. Getting 8 to 10 intervals is ideal because
it can you enough space in grouping the data. It is not so small and it is not so big.

In the example, you can see that the data has already been arranged from lowest to
highest value. The lowest score is 9 and the highest is 48. That gives us

Range = HV – LV

Range = 48 – 9 = 39

This range is close to 40 and we can divide it by 8 or 10 easily... but to have an

easier table, lets divide it by 8. Giving us
Class interval =

𝑟𝑎𝑛𝑔𝑒
𝑐𝑙𝑎𝑠𝑠 𝑠𝑖𝑧𝑒 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙𝑠

39
𝑐𝑙𝑎𝑠𝑠 𝑠𝑖𝑧𝑒 = 8

𝑐𝑙𝑎𝑠𝑠 𝑠𝑖𝑧𝑒 = 4.875

Since the result is a decimal value, we round it off to the nearest whole number, giving us a
class size of 5.

To start the frequency table, we need to construct the class intervals. We take the smallest
value in the given, 9 and then count up to 4 more values.

Our table should look like this.

Class Interval Frequency

9 – 13 3
14 – 18 5
19 - 23 5
24 – 28 2
29 – 33 7
34 – 38 2
39 – 43 2
44 – 48 4
Total = 30
The frequency should be the tally of the values that are within the created class intervals
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9 11 12

14 15 15 16 17

19 20 20 20 22

26 28

29 30 30 30 30 31 33

35 37

40 43

45 46 47 48

Note: The data now becomes “grouped” inside the class intervals and should tally or
correspond to the present distribution table.

Here are few easy steps in creating a frequency distribution table.

1. Arrange your data in ascending order (lowest to highest).
2. Find the range.
3. Determine the class size by setting the proposed number of intervals you need to
present. (preferably the class size should be odd/the number of intervals can be
greater than 4)
4. Start with the lowest class interval and go up until you reach the highest score/value
in the distribution.
5. Plot your frequencies accordingly and complete the table.

Class Interval – it is the tabular set where values are tallied as frequencies and it has a lower
limit and an upper limit.

Lower limit Upper Limit

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Lower Limit – is the value that indicates the lowest possible value inside a class interval
Upper Limit – is the value that indicates the highest possible value inside a class interval

Now that we have completed our first frequency distribution table, lets add in a few
details. Since we have grouped our data we have actually “lost” the actual scores we had
before we transformed the data into the table. This prompts us to have a value that represent
the whole class interval and that is the class mark.

Class mark – it is the midpoint of a class interval. It represents the average value within an
interval.

Cumulative Frequency – is the sum of all the frequencies for any preceding class interval.
It sums up all the frequencies of intervals above it (<).

class marks cummulatitive frequency

Independent Activity 1

Direction: Construct the appropriate column of class intervals given the following conditions.

Given:
highest score = 70
lowest score = 9
class size = 9

Independent Assessment 1

Direction: Complete the table that follows. Supply the missing value for the class mark and
cumulative frequencies.

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 Class Interval Frequency Class Mark Cumulative
Frequency
24 - 29 4 26.5
30 – 35 6 10
36 - 41 8
42 - 47 12
48 - 53 7
54 - 59 3

Independent Activity 2

Direction: Read and answer the given condition below.

Start a list of hobbies for yourself and ask another of other friends to do the same and
list down their hobbies as well. Make sure that everyone gets to list down their hobby. Once
you have networked at least 8 friends. Compare notes and find out what hobbies you have in
common. Make a list of frequencies for commonly shared hobbies.

Independent Assessment 2

Direction: Complete the table below. Supply the missing values for the frequency, class
interval, class mark and cumulative frequencies.

Class Interval Frequency Class Mark Cumulative

Frequency
24 – 26 4 25 4
27 – 29 5 28
18
6
36 – 38 5
4 42

Independent Activity 3

Direction: Arrange the following data from highest to lowest and then determine the range.

11 12 14 16

17 34 22 15

24 24 42 48

63 12 55 44

38 50 18 29

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Independent Assessment 3

Direction: Given the following data, complete the Frequency Distribution Table. Use a class
size of 7.

42 43 44 44 46
48 49 50 51 52
56 58 59 60 60
60 60 62 63 68
70 72 72 75 76
78 81 82 85 86
87 88 88 89 90

Class Interval Frequency Class Mark Cumulative

Frequency
42 - 48 45
49 – 55

35

Let us summarize what you have learned by completing the statements below.

I have learned that.....

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 As you can now use and construct the Frequency Distribution Table, try and reflect on
its uses outside the school and how it can be applied to daily activities. As one example we
can automatically see it on charts and tables in hospitals and government offices. What else
can you think of? Put your answer on the space provided.

Part I. Direction: Complete the missing values for the table below, for items 1-5.

CLASS INTERVAL FREQUENCY CLASS MARK <CF

31 – 35 5 33 5
36 – 40 8 38 #4
41 – 45 12 #3 25
46 – 50 22 48 47
51 – 55 #2 53 #5
#1 8 58 65

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Part II. Direction: Multiple Choice. Write the letter of the correct answer on the space provided

________ 1. What type of data does the Frequency Distribution Table have?
a. grouped data b. ungrouped data
c. actual values d. graded values

________ 2. The class interval contains limits – which of the of these determine the highest
possible value in an interval?
a. class mark b. lower limit
c. upper limit d. class boundary

________ 3. If the range is 80, and you are asked to make 8 class intervals, what would be
the appropriate class size?
a. 5 b. 10
c. 12 d. 8

________ 4. In a distribution table the presentation of data is always in what form?

a. graph b. illustrative
c. tabular d. textual

________ 5. What do you call the difference between the highest value minus the lowest value
in a distribution?
a. mean b. range
c. class interval d. class boundary

________ 6. It refers to the size of the class interval.

a. class interval b. class boundary
c. class size d. lower limit

Refer to the table below for items 7-10

CLASS INTERVAL FREQUENCY CLASS MARK <CF
31 – 35 6 33 6
36 – 40 9 38 15
41 – 45 15 43 30
46 – 50 6 48 36
51 – 55 4 53 40

__________ 7. How many respondents were in the distribution?

a. 10 b, 20
c. 25 d. 40
__________ 8. What class interval has the highest frequency?
a. 41 – 45 b. 46 – 50
c. 51 – 55 d. 36 – 40

__________ 9. What class interval has the lowest frequency?

a. 41 – 45 b. 31 – 35

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 c. 51 – 55 d. 36 – 40

__________ 10. Where can you find the highest possible score?
a. first interval b. second interval
c. middle interval d. last interval

Try this one out by completing all the missing values in the table below.

Class Interval Frequency Class Mark Cumulative

Frequency
18 – 23 2
24 – 29 3 5
30 - 35 7
12
20
15
5
70

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Independent Activity 3
63 55 50 48 44
42 38 34 29 24
24 22 18 17 16
15 14 12 12 11
Range = 63 – 11
Range = 52
Independent Assessment 3
Class Frequency Class Cumulative
Interval Mark Frequency
42 - 48 6 45 6
49 – 55 4 52 10
56 – 62 8 59 18
63 – 69 2 66 20
70 – 76 5 73 25
77 – 83 3 80 28
84 – 90 7 87 35
What I have learned
Answers may vary
Assessment
Part I 1. 56 - 60
2. 10
3. 43
4. 13
5. 57
Part II 1. A
2. C
3. D
4. C
5. B
6. C
7. D
8. A
9. C
10. D
Additional Activity
Class Frequency Class Cumulative
Interval Mark Frequency
18 – 23 2 20.5 2
24 – 29 3 26.5 5
30 - 35 7 32.5 12
36 – 41 12 38.5 24
42 – 47 20 44.5 44
48 – 53 15 50.5 59
54 – 59 5 56.5 64
60 - 65 6 62.5 70
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What I Know
1. B
2. D
3. C
4. A
5. B
6. A
7. A
8. C
9. C
10. A
11. D
12. D
13. B
14. C
15. B
Independent Activity 1
CLASS INTERVAL
9 – 17
18 – 26
27 – 35
36 – 44
45 – 53
54 - 62
63 - 71
Independent Assessment 1
Class Frequency Class Cumulative
Interval Mark Frequency
24 - 29 4 26.5 4
30 – 35 6 32.5 10
36 - 41 8 38.5 18
42 - 47 12 44.5 30
48 - 53 7 50.5 37
54 - 59 3 56.5 40
Independent Activity 2
Answer may vary
Independent Assessment 2
Class Frequency Class Cumulative
Interval Mark Frequency
24 – 26 4 25 4
27 – 29 5 28 9
30 – 32 18 31 27
33 – 35 6 34 33
36 – 38 5 37 38
39 – 41 4 40 42
 References

Mercado, Jesus P. Next Century Mathematics Quezon City: Phoenix Publishing House,
Inc., 2016

Cue Learn Pvt. Ltd. Cuemath. Cue Learn Private Limited is a company duly incorporated
under the provisions of the Companies Act, 1956. https://www.cuemath.com/jee/

Toppr Technologies Private Limited, incorporated under the Companies Act, 2013. https://
www.toppr.com/guides/maths/statistics /

Eric Weisstein. Wolfram Mathworld. https://mathworld.wolfram.com/frequecy

table.html

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For inquiries or feedback, please write or call:

Department of Education, Schools Division of Bulacan

Curriculum Implementation Division
Learning Resource Management and Development System (LRMDS)
Capitol Compound, Guinhawa St., City of Malolos, Bulacan

Email Address: lrmdsbulacan@deped.gov.ph

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