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MATHEMATICS
Quarter 4 – Module 3
Frequency Distribution

NegOr_Q4_Mathematics7_Module3_v2
Mathematics – Grade 7
Alternative Delivery Mode
Quarter 4 – Module 3: Frequency Distribution
Second 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: MARCELO B. SASTRILLO
Editor: CONCORDIO J. ALAS-AS JR.
Reviewer: ROLANDO B. ABRASADO
Illustrator:
Layout Artist: ANGELICA G. BAJAR
Management Team: Senen Priscillo P. Paulin, CESO V Elisa L. Baguio, Ed.D.
Joelyza M. Arcilla, EdD, CESE Rosela R. Abiera
Marcelo K. Palispis, JD, EdD Maricel S. Rasid
Nilita L. Ragay, Ed.D Elmar L. Cabrera

Printed in the Philippines by ________________________

Department of Education –Region VII Schools Division of Negros Oriental

Office Address: Kagawasan, Ave., Daro, Dumaguete City, Negros Oriental

Tel #: (035) 225 2376 / 541 1117
E-mail Address: negros.oriental@deped.gov.ph
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 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 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. And 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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 I
This module was designed to provide you with fun and meaningful
opportunities for guided and independent learning at our own pace and time. It is
designed to help you organize data using frequency distribution table.
In this learning module you will learn to cite the importance of
gathering/ collecting data in real life situation.

Choose the best answer among the given choices.

1. ___________ is the difference between the highest data value and the lowest data value.
A. Domain B. Range C. Class Interval D. Frequency

2. __________ refers to the difference between two consecutive lower limits.

A. class width B. lower limit C. upper limit D. range

3. __________refers to the smallest data value that can be included in a class.

A. upper limit B. lower limit C. frequency D. table

4. _______ refers to the values and their frequencies (how often each value
occurs).
A. Frequency C. class width
B. frequency distribution D. range

5. ___________ is how often something occurs.

A. frequency C. lower limit
B. upper limit D. range

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 ’s In

POINTS TO REMEMBER!

➢ Frequency is how often something occurs.

➢ Frequency distribution refers to the values and their frequencies (how often each value
occurs).

➢ Range is the difference between the highest and the lowest value.

➢ Lower limit refers to the smallest data value that can be included in a class.

➢ Upper limit refers to the largest data value that can be included in a class.

➢ Class with refers to the difference between two consecutive lower limits.

’s New

Hello! Let’s say you survey a number of households and find out how many pets
they own. The results are 3,0,1,4,4,1,2,0,2,2,0,2,0,1,3, 1,2,1,1,3. Looking at that string of
numbers boggles the eye; a frequency distribution table will make the data easier to
understand.
Today we will organize and present data using Frequency Distribution Table.
Together, we will answer questions such as “What is a Frequency Distribution Table?”,
“How to make a Frequency Distribution Table?”,
This lesson focuses on the use of frequency distribution tables as a way of
organizing and presenting data so that it makes more sense.

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 is It

A. Frequency
Frequency is how often something occurs.

(www.pinterest .com n.d.)

Example: Sam played football on:
● Saturday Morning
● Saturday Afternoon
● Thursday Afternoon

The frequency was 2 on Saturday, 1 on Thursday and 3 for the whole week.

B. Frequency Distribution
By counting frequencies, we can make a Frequency Distribution table.
How to make Frequency Distribution Table?
a. Frequency Distribution table for Ungrouped Data

Example1: Goals
Tally marks are often used to make a frequency distribution table. For example,
Sam’s team has scored the following numbers of goals in recent games
2, 3, 1, 2, 1, 3, 2, 3, 4, 5, 4, 2, 2, 3.

Sam put the numbers in order, then added up:

● how often 1 occurs (2 times),
● how often 2 occurs (5 times),
● etc,

And wrote them as a Frequency Distribution table.

Steps:

To make the frequency distribution table, first write the categories in one column ( Score ).
Score Tally Frequency
1
2
3
4
5

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Next, tally the numbers in each category. For example, the number three appears four times in
the list so, put four tally marks “IIII”.
Score Tally Frequency
1 II
2 IIII
3 IIII
4 II
5 I
Finally, count up the tally marks and write the frequency in the final column. The frequency is
just the total. You have two tally marks for the score of “1”, so put 2 in the last column.
Scores:
1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5

Score Tally Frequency

1 II 2
2 IIII 5
3 IIII 4
4 II 2
5 I 1

From the table we can see interesting things such as

● getting 2 goals happens most often
● only once did they get 5 goals

Here is another example:

Example 2. Notebooks
These are the numbers of notebooks sold at a local shop over the last 10 days:
22, 20, 18, 23, 20, 25, 22, 20, 18, 20

Let us count how many of each number there is:

Notebooks Sold Tally Frequency

25 I 1
24 0
23 I 1
22 II 2
21 0
20 IIII 4
19 0
18 II 2

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Frequency Distribution table for Grouped Data
It is also possible to group the values.
Example 1.
The data represent the ages of 40 women when each had a boyfriend women when they each had
a boyfriend. Construct a group frequency distribution with five classes.
18 20 20 20 20 21 20 17 19 20
13 18 22 26 20 19 22 15 18 27
16 23 24 17 25 24 16 20 26 15
21 17 23 16 21 17 26 16 23 19

How to construct a group frequency distribution table?

Step 1. Find the range. The range is the highest data minus the lowest data.
The highest age is 27 and the lowest age is 13.
Range = Highest – Lowest
= 27 -13
= 14

Step 2. Decide the number of groups or classes. Figure out how many classes (categories) you
need. There are no hard rules about how many classes to pick but there are a couple of general
guidelines.
⦁ Pick between 5 and 20 classes.
⦁ Make sure you have a few items in each category. For example, if you have 20 items, choose 5
(four items per category), not 20 classes (which would give you only 1 item per category).

In this example, the number of groups or classes is 5.

Classes : 5

Step 3. Divide the range by the number of desired classes.

To find the class width:

𝒓𝒂𝒏𝒈𝒆 𝟏𝟒
Class width = 𝒄𝒍𝒂𝒔𝒔𝒆𝒔 = 𝟓
= 2.8 or approximately round up to 3.

Therefore we have 5 groups or classes with 3 data values per group.

Our goal here is to divide the data into 5 groups or classes, each containing 3 numbers

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 ( https://www.youtube.com/watch?=7CcmBxf7luo n.d.)
Our starting point is 13 which is the lowest age. Remember that our class width is 3 meaning
there are 3 numbers in each group. Let’s count; 13, 14, 15. Our first class is 13 – 15.

( https://www.youtube.com/watch?=7CcmBxf7luo n.d.)
The left member is the lower limit and the right member is the upper limit.

To get the next lower limit, just add the class width to the previous lower limit.
13 + 3 = 16, 16 + 3 = 19, 19 + 3 = 22, 22 + 3 = 25.

To get the next upper limit, just add the class to the previous upper limit.
So, 15 + 3 = 18, 18 + 3 = 21, 21 + 3 = 24, 24 + 3 = 27.

( https://www.youtube.com/watch?=7CcmBxf7luo n.d.)

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Now, we have 5 classes in decreasing order. Each contains three data values. The classes are
arranged in decreasing order. 25 – 27 is the highest class interval. 13 – 15 is the lowest class
interval.
A frequency is the number of times a data value occurs. Let’s count the number 13, 14, 15 occur
in in our data. It is 3. How about 16 – 18? It is 11. How about 19 - 21? The answer is 14. How
about 22 -24? Its is 7. How about 25 – 27? The number of data is 5. The add the frequency of
each class. 5 + 7 + 14 + 11 + 3 = 40. The total of the frequency represents the number women
included in the sample.

( https://www.youtube.com/watch?=7CcmBxf7luo n.d.)

To construct a grouped frequency distribution table, find the highest data value and the lowest
data value. Subtract the lowest data value from the highest data value. Divide it by the number of
desired class to obtain the class width. Add the class width minus 1 to get the upper limit. Add
the class with to the lower limit to get the next lower limit and add also tha class width to get the
next upper limit. Then, find the frequency of each class then add the total frequency.

Another example
Example 3. The following is a list of shoe sizes of 35 boys.

7 5 4 4 6 5 4

8 5 5 4 3 5 6

5 3 6 3 2 8 5

6 6 7 4 7 4 5

4 4 2 5 5 6 4

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 a) What information can you get from the above list?
b) What does the list tell us?
c) The list above does not tell us anything. So, what do we do with the list?
We construct a table with three columns. The shoe sizes may be grouped as follows: 2-3, 4-5, 6-
7, and 8-9…Then we refer to our list and go down each column and make a mark for each figure
or number in the tally table. For boundary sizes, we can use the rule that we include the lower
bound in the interval but not the upper bound.

This is how to fill in each column of the table using the data given)

Shoe size Tally Frequency

2-3 IIII 5
4-5 IIII IIII IIII IIII 19
6 -7 IIII IIII 9
8 -9 II 2
Total 35

After tallying, we count the tally marks in each row and put the number in the last column.

’s More

The following is the number of pets each household owned.

1 3 9 5 2

8 9 2 6 2

5 6 1 2 4

6 3 3 3 3

Tasks:

1. Organize the data above using a

a. Ungrouped Frequency Distribution table.
b. Grouped Frequency Distribution table.

2. Write interesting things you can see from the data after you have organized in a
Frequency Distribution table.

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 I Have Learned

Instruction: Make a journal to manifest your understanding about the topic. You can start it by
following the format below.

I have learned that the steps in constructing a Frequency Distribution table are
____________________________________________________________
____________________________________________________________
I have realized that after data gathered in any ways
____________________________________________________________
____________________________________________________________

I Can Do

List down things inside your home and categorize which they belong. Make a frequency
distribution table from the data and tell something interesting about it.
Rubrics: (For each frequency table)

Accuracy: 3pts Completeness: 3pts Artistry: 2pts Neatness: 2pts Total= 10pts

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Organize the following data using:

a. Ungrouped frequency distribution table.

b. Grouped frequency distribution table.

Number of red dresses each student owned.

1 3 5 2 1 4 2

4 7 3 8 8 1 1

2 5 3 3 2 6 9

1. You have conducted a survey on a number of households and found out how many pets

they owned. The results are 3,0,1,4,4,1,2,0,2,2,0,2,0,1,3,1,2,1,1,3. Construct an ungroup

frequency distribution table.

2. Construct a group frequency distribution table of the data below.

Raw data of Mathematics Summative Test Scores

of 45 Grade 7 Students.

43 44 34 35 36 37 38
40 41 43 45 42 41 37
42 35 36 37 37 28 30
43 45 46 48 34 36 36
41 42 43 42 42 32 33
38 36 34 32 31 29 30
39 38 40

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References
n.d. https://www.youtube.com/watch?=7CcmBxf7luo.
n.d. https://www.mathsisfun.com/data/frequency-distribution.html.
n.d. https://www.statisticshowto.com/probability-and-statistics/descriptive-statistics/frequency-
distribution-table/.
n.d. www.pinterest .com.

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For inquiries or feedback, please write or call:

Department of Education – Schools Division of Negros Oriental

Kagawasan, Avenue, Daro, Dumaguete City, Negros Oriental

Tel #: (035) 225 2376 / 541 1117

Email Address: negros.oriental@deped.gov.ph
Website: lrmds.depednodis.net