Lesson plan in mean for grouped data.

1. Republic of the Philippines
Department of Education
MIMAROPA Region
Division of Occidental Mindoro
DETAILED LESSON PLAN IN MEAN OF GROUPED DATA
FOR DEMONSTRATION TEACHING
December 1, 2019
I. OBJECTIVES
A. Content Standards
The learner demonstrates understanding of key concepts, uses and importance of
Statistics, data collection/gathering and the different forms of data representation, measures of
central tendency, measures of variability, and probability.
B. Performance Standards
The learner is able to collect and organize data systematically and compute accurately
measures of central tendency and variability and apply these appropriately in data analysis and
interpretation in different fields.
C. Learning Competencies
The learner calculates the measures of central tendency of ungrouped and grouped data.
(M7SP-IVf-g-1)
Specific Objectives:
At the end of the lesson, the students should be able to:
A. state the formula in finding the mean of grouped data;
B. find the mean of grouped data; and
C. solve problems involving mean of grouped data.
II. CONTENT
Topic: Averages: Mean, Median and Mode
Sub-topic: Mean of Grouped Data
III. LEARNING RESOURCES
References:
1. Learner’s Module in Mathematics 7 pp. (245-247)
2. Moving Ahead with Mathematics II pp. (251-253)
3. Dynamic Math II pp. (255-256)
4. Making Connections in Mathematics IV pp. 357-360
Materials: Visual aids and slide deck presentation
IV. PROCEDURES
Teacher’s Activity Students’ Activity
Preliminary Activity:
1. Prayer
Before we start, let’s ask the guidance of
our Lord.

2. In the name of the father, and of the Son,
and of the Holy Spirit. Amen.
God Holy Spirit.
In the name of the father, and of the Son,
and of the Holy Spirit. Amen.
Good morning class!
2. Checking of Attendance
Who are the absentees for today?
Ms. Bandiola kindly pass the list of the
absentees for today.
Okay, thank you.
3. Checking of Assignment
Did I give you an assignment?
Bring out your assignment and pass them
forward. I’ll be the one to check your
assignment.
A. Reviewing previous lessonor presenting
the new lesson
Before we proceed to our new lesson, let
us have a recap of our last topic.
What was our last topic all about?
Yes, Jyron.
Very good! What is the formula for mean
of ungrouped data?
Yes, Franklin.
You’re right. What is the formula for
median of a data set having an odd number of
scores?
Yes, Angel.
Correct! How about the formula for
median of a data set having an even number of
scores?
Yes, Joemil.
That’s right. How will you find the mode
of ungrouped data?
Yes, Franklin.
All for love of Thee.
Good morning Ma’am.
Here is the list, Ma’am.
Yes, Ma’am.
Ma’am.
Our last topic was all about mean, median
and mode of ungrouped data.
Ma’am.
x =
N
X

Ma’am.
The median for an odd number of scores or
items is the middle number when the scores or
items are arranged in order of magnitude.
Ma’am.
If the number of scores is even, the median
is determined by computing the average of the
two middle numbers.
Ma’am.

3. Amazing! Now, I know that you really
understand our lesson yesterday. Let’s proceed
to our new lesson.
B. Establishing a purpose for the lesson
Class do you want to play a game?
Okay! This game is entitled “Add and
divide me”. This game is good for 5 minutes. I
have here 3 boxes, each box contains chips
with numbers written on each of them. All you
have to do is to get the chips, then get the sum
of the numbers written on the chips. Lastly, get
the average. You will answer by group. The
first three rows in my left will be the group 1,
the first three rows in my right will be the
group 2, and the rest will be the group 3. You
will be given a cartolina per group wherein you
will write your answer. The group who will
gain the highest score will be the winner. The
winner will receive a prize next meeting.
Is the instruction clear?
Once I give my go signal, you may start.
Here are the boxes. This is for the group
1, group 2, and group 3.
Group 1:
10 15 10 10 12 15 20 15 20 20
12 21 15 15 10 20 15 20 20 22
20 25 11 10 10 10 12 10 15 10
Group 2:
6 6 5 15 3 3 10 9 15 14
12 13 10 10 15 14 14 13 15 15
5 5 5 9 9 10 10 10 10 10
Group 3:
12 10 5 11 11 10 10 12 8 12
11 5 5 20 15 15 10 20 15 20
21 22 22 21 12 15 10 10 25 25
Ready set go!
Are you done class?
Alright. Post your work on the board.
Get the number which occurs most
frequently in a set of numbers.
Yes, Ma’am.
Yes, Ma’am.
(All groups will start to work.)
Yes, Ma’am.
Group 1:
10+15+10+10+12+15+20+15+20+20+12+21+
15+15+10+20+15+20+20+22+20+25+11+10+
10+10+12+10+15+10= 450
=
30
450
= 15
Group 2:
6+6+5+15+3+3+10+9+15+14+12+13+10+10+
15+14+14+13+15+15+5+5+5+9+9+10+10+10
+10+10 = 300

4. Okay, all of your answers is correct! Did
you have a hard time getting the sum of the
data?
Why do you think it is hard for you to get
the sum of the data?
Yes, Jyron.
Correct! It is difficult to add all those
data in a short period of time. But, what do you
observe on the data?
Perfect! So, what is the technique that
you should do to make it easier?
Yes, Jayvon.
Awesome! Instead of adding the data
repeatedly, count the number of appearance of
the data or its frequency, then multiply the data
by it.
C. Presenting examples/instances of new
lesson
In our previous activity, we applied the
concept of averaging and it is related to our
lesson for today.
Now, you will watch a short video. I
want you to watch and listen carefully. If you
want to take down some notes, you may write
it on your notebook.
(The video will be played.)
Based on the video, what is our topic for
today?
Correct!
Presentation of Instructional Objectives:
Altogether, please read the objectives?
At the end of the lesson, the students should
be able to:
=
30
300
= 10
Group 3:
12+10+5+11+11+10+10+12+8+12+11+5+
5+20+15+15+10+20+15+20+21+22+22+21+
12+15+10+10+25+25 = 420
=
30
420
= 14
Yes, Ma’am.
Ma’am.
It is because the number of data is too many.
Some data was repeated.
Ma’am.
We should get the frequency of each data,
then we will just multiply each data by its
frequency.
(The students will watch the video.)
Our topic for today is all about the mean of
grouped data.

5. A. state the formula in finding the mean
of grouped data;
B. find the mean of grouped data; and
C. solve problems involving mean of
grouped data.
Those objectives serve as our target
which must be achieved at the end of the
lesson.
D. Discussing new concepts and practicing
new skills #1 1. Discussion:
When the number of data is at least 30, we
can’t use the formula of ungrouped data to find
the mean. Instead, we will now use the
formula for grouped data.
Let us discuss the mean of grouped data.
When data had been grouped in a
frequency distribution, the midpoint of each
class is used as an approximation of all values
contained in the class. The formula for sample
mean is:
x =
N
fx

Where x = Mean
∑ = Summation
f = frequency
x = Class mark/ midpoint
N = Total number of data
There are steps in computing the mean of
grouped data.
1. Make a frequency distribution for data.
Step 1: Find the range:
Range = highest score – lowest score
Step 2: Decide on the class intervals which
is appropriate to the given set of data.
Step 3: Get the class size ( i ) :
Range
Class size =
Number of class interval
Class size is being rounded to a whole
number.
Step 4: Lowest class
Find the lower limit of the lowest class,
it must be a multiple of the class size.
Step 5: Classes
Add the class size to the lower limit of
the lowest class. List all classes until the
highest class contains the highest score.
At the end of the lesson, the students should
be able to:
A. state the formula in finding the mean
of grouped data;
B. find the mean of grouped data; and
C. solve problems involving mean of
grouped data.

6. Step 6: Make a tally of each score
corresponding to each class interval.
Let us make a frequency distribution of
Scores of 30 students in a Mathematics test.
20 25 35 30 10 20
40 20 15 25 20 40
25 30 15 20 49 20
15 25 25 19 20 12
5 20 20 15 5 20
Step 1: Range = 49-5
= 44
Step 2: Class interval = 9
Step 3: Class size =
9
44
= 4.88
= 5 (rounded off)
Step 4: Lowest class = 5-9
Step 5: Classes
45-49
40-44
35-39
30-34
25-29
20-24
15-19
10-14
5-9
Step 6: Frequency distribution
Scores of 30 students in a Mathematics test
Classes Tally Frequency
45-49 | 1
40-44 || 2
35-39 | 1
30-34 || 2
25-29 |||| 5
20-24 ||||-|||| 10
15-19 |||| 5
10-14 || 2
5-9 || 2
E. Discussing new concepts and practicing
new skills #2
2. Make a table showing the frequency
distribution with class mark and fx column of
30 scores in Mathematics test.

7. Classes Frequency
f
Midpoint
x
Product
fx
45-49
40-44
35-39
30-34
25-29
20-24
15-19
10-14
5-9
1
2
1
2
5
10
5
2
2
47
42
37
32
27
22
17
12
7
47
84
37
64
135
220
85
24
14
N = 30  
fx 710
3.Using
=
30
710
X = 23. 66
Mean class is where the computed mean
belongs. So, what is the mean class?
Yes, Rainier.
Very good! Do you have questions?
Okay, if there is no question let us have an
exercise. You will answer it by group. Your
previous group will do. Answer will be written
on a cartolina. I need one volunteer from each
group to discuss their work in front.
Is everything clear?
F. Developing mastery (Leads to Formative
Assessment)
1. Consider the given frequency
distribution of test score in Algebra below, find
the mean.
Scores frequency (f) x fx
45-49
40-44
35-39
30-34
25-29
20-24
15-19
10-14
3
5
10
10
10
5
5
2
Are you done?
Okay, post your work on the board.
Ma’am.
The mean class is from 20 to 24.
None, Ma’am.
Yes, Ma’am.
Yes, Ma’am.
X =
fX
N

8. Is there any question?
G. Finding practical applications of
concepts and skills in daily living
Now, let us apply our lesson in real life
situation. I will flash some pictures to help you
relate our lesson for today.
Based on the picture, where can we apply
mean? Anyone?
Yes, Marben.
Correct! How about this?
Yes, Alfred.
You are right. Who can guess this one?
Yes, Trisha.
That is right. All your answers are correct.
Class, indeed, you are all excellent!
H. Making generalizations and abstractions
about the lesson
Let us sum up your lesson for today.
What is the formula in finding the mean
of grouped data?
Yes, James.
(All group will post their work on the board,
and group 1 will start to report until group 3.)
Scores frequency (f) x fx
45-49
40-44
35-39
30-34
25-29
20-24
15-19
10-14
3
5
10
10
10
5
5
2
47
42
37
32
27
22
17
12
141
210
370
320
270
110
85
24
N = 50
 1590
fx
x =
N
fx

=
50
1590
x = 31.8
None, Ma’am.
Ma’am.
We can apply mean by getting the grades of
the students every grading period.
Ma’am.
It can also be used to find the winner in a
competition.
Ma’am.
Mean can also be used to know who passed
the board exam.
Ma’am.
x =
N
fx


9. Correct! In making a frequency
distribution, there are 6 steps. Kindly give the
first step.
Yes, Shelby.
Correct! How will we find the range?
Yes, Franklin.
You’re right. What is the next step?
Yes, Jyron.
Very good! What is the third step?
Yes, Jeric.
Correct! How will you get the class size?
Yes, Franklin.
You’re correct! What else?
Yes, Angel.
Perfect! What is the fifth one?
Yes, Dave.
Awesome! And kindly give the last one.
Yes, Lovely.
Perfect! After you have made a
frequency distribution, what will you do next?
Yes, Nicole.
Amazing! Class, when will you use the
formula for grouped data in finding the mean?
Yes, Trisha.
Awesome! I’m glad that you really listen
to our discussion.
Ma’am.
The first step is to find the range.
Ma’am.
Range = Highest score – lowest score
Ma’am.
Decide what should be the class interval.
Ma’am.
The third step is to solve for the class size.
Ma’am.
Range
Class size =
Number of class interval
Ma’am.
The next step is to find the lower limit of the
lowest class. And the lower limit must be a
multiple of the class size.
Ma’am.
It is to list all classes until the highest class
contains the highest score.
Ma’am.
Draw a frequency distribution with three
columns and tally each score corresponding to
each class interval. In the third column, write
the number of tallies or frequency.
Ma’am.
Make a table showing the frequency
distribution of the score with class mark (x)
and fx column, then compute for the mean.
Ma’am.
We will use it when the number of data is at
least 30.

10. Values Integration:
Okay, let me give you a situation.
Your barangay is being hit by a typhoon.
Stocks are limited due to the delay of the
delivery of food and other necessities coming
from other barangays. There are 20 households
in your barangay. Jolindon, and Bandiola
family has 5 family members, Romero, Barolo,
Abarquez, Vergera, and Candor family has 2,
Benoza, Samson, Sampilo, Dela Vega and
Basbas family has 4, Talam, Roldan, and Mina
family has 10, Benoza, Sese, Castillo, Capuno
and Camonino family has 6. The problem to be
solved is to determine the estimated number of
stocks which will be given to every households
in your barangay. What should be done to
solve it?
Yes, Franklin.
That is right! Now, What is the sum of the
family members?
Yes, James.
Correct! Then, what should be done next?
Yes, Shelby.
Perfect! So what numbers will you divide?
Yes, Rex.
Correct! Therefore, what is the number of
stocks per households?
Yes, Jessica.
You are right!
What values can you get from the given
situation?
Yes, Rex.
You are correct. What else?
Yes, Elgen.
Very good! What else? Anyone?
Yes, Jyron.
Ma’am.
We must get the total number of family
members in 20 households.
Ma’am.
The total number of family members in 20
households is 100.
Ma’am.
Get the average by dividing the number of
family members by the number of households.
Ma’am.
100 and 20. 100 divided by 20 is equal to 5.
Ma’am.
Every household in the barangay will receive
5 stocks.
Ma’am.
We have to be fair all the time. Especially
during crisis, we have to be just and equal.
Ma’am.
We should extend help to those who is in
need.
Ma’am.

11. Fantastic! During your group activity or in
the discussion, what values did you perform?
Amazing! I am happy that you have learned
a lot of values for today’s lesson.
I. Evaluating learning
1. Below is a table showing the frequency
distribution of 30 students who took the
entrance test in San Jose National High School.
Complete the table and find the mean and the
mean class.
N = 30
Classes Frequency x fx
90-94
85-89
80-84
75-79
70-74
65-69
60-64
2
5
10
2
5
0
6
J. Additional activities for application or
remediation
Fill in the table.
1. The following distribution of the
scores which 500 students obtained in an
achievement test in Mathematics 7 is given
below:
We can share what we have and make good
deeds.
The students answer varies: cooperation,
accuracy and honesty.
Answer Key:
N = 30 ∑fx = 2325
Classes Frequency x fx
90-94
85-89
80-84
75-79
70-74
65-69
60-64
2
5
10
2
5
0
6
92
87
82
77
72
67
62
184
435
820
154
360
0
372
Mean:
x =
N
fx

=
30
325
,
2
= 77.5
Mean class = 75-79

12. IV. REMARKS
V. REFLECTION
A. No. of learners who earned 80% in the
evaluation
B. No. of learners who require additional
activities for remediation who scored
below 80%
C. No. of learners who have caught up with
the lesson
D. No. of learners who continue to require
remediation
E. Which of my teaching strategies worked
well? Why did this work?
F. What difficulties did I encounter which my
principal or supervisor can help me solve?
G. What innovation or localized materials did
I use or discover which I wish to share with
other teachers?
Prepared by:
MARISSEL A. LIM
Teacher I
Corroborated by:
DR. ANNABELLE A. GORDONAS JOHNALY S. ADARLO
PUP Manila/PCPD Trainer Principal I
Payompon Elementary School
DYLENE R, EJE MARK ANTHONY G. EJE
Principal I Principal I
Balansay Elementary School Marikit Elementary School
ROSALIE A, CASTRO DANTE D. SALES
Master Teacher I Master Teacher I
Central National High School Central National High School
Scores
freque
ncy (f)
Class
Mark
(x)
fx
85-99
70-84
55-69
40-54
25-39
10-24
32
115
147
92
70
44
N = 500