The document provides instructions for teaching students about measures of central tendency (mean, median, mode) using ungrouped data. It outlines objectives, subject matter, materials, and procedures for the lesson. The teacher's activity is to define and provide examples to calculate the mean, median, and mode. The students' activity is to practice calculating these measures and describing data sets in terms of them. The lesson concludes with an assignment for students to find the mean, median, and mode of additional data sets.

1. I. Objectives: At the end of the lesson, the students are expected to:
a. define the mean, median and mode;
b. find the mean, median and mode of the given set of the data;
c. describe the data in terms of the mean, median and mode.
II. Subject Matter: “Measures of Central Tendency of Ungrouped Data”
Reference: Mathematics 8, Learner’s Module, pp. 491-496
Skills: Computing and Analyzing
III. Materials: books, visual aids, cartolina strips
IV. Procedure: Developmental Method
Teacher’s Activity Student’s Activity
A. Preparation
a. Review
Class yesterday we discussed about
summation.
So, as you can see on the board there
are sets of data given.
So, who would like to come to the
board and solve the given data?
X1=85 X3=88 X5=87 X7=84 X9=94
X2=80 X4=83 X6=89 X8=80 X10=90
Find:
a. ∑ 𝑥10
𝑖=1
b. ∑ 𝑥5
𝑖=1
a. ∑ 𝑥10
𝑖=1 = x1 + x2 + x3 + . . . + x10
= 85 + 80 + 88 + 83 + 87 + 89 + 84 + 80
+ 94 + 90
∑ 𝑥10
𝑖=1 = 860
b. ∑ 𝑥5
𝑖=1 = xi + . . . + x5
= 85 + 80 + 88 + 83 + 87
∑ 𝑥5
𝑖=1 = 423

2. c. ∑ 𝑥10
𝑖=6
b. Motivation
Class the data from X1 to X10 are 85, 80,
88, 83, 87, 89, 84, 80, 94 and 90.
Arranging these in increasing order,
that is from least to greatest
80,80,83,84,85,87,88,89,90 and 94.
Class, what do you observe with the
data?
Yes,_____________
That’s right!
Class if I am going to use these data
80, 80, 83, 84, 85, 87, 88, 90 and 94 as the math
grades of 10 students. And aside from adding
these data with the use of summation method,
do you know that these data can also be
summarized into a single number or single
data?
B. Presentation
So be with me this morning class, as I
discuss to you about “Measures of central
Tendency (Ungrouped Data)”.
Everybody read!
a. Statement of the aim
Class listen carefully because after
my discussion you will be asked to define the
mean, median and mode, find the mean,
median and mode of the given set of data and
lastly, you will be asked to describe the data in
terms of the mean, median, and mode.
Am I understood class?
c. ∑ 𝑥10
𝑖=6 = x6 + x7 + . . . + x10
= 89 + 84 + 80 + 94 + 90
∑ 𝑥10
𝑖=6 = 437
The data given are all number.
No, ma’am
“Measures of Central Tendency of Ungrouped
Data”
Yes, ma’am

3. C. Developmental Proper
Okay class there are three measures of
central tendency, first one is the mean.
Mean – is the most commonly used measure of
central tendency. It is used to describe a set of
data where the measures cluster or concentrate
at a point. It is found by adding the values of
the data and dividing by the total number of
values.
It is given with the formula
𝑥̅ =
Ʃ𝑥
𝑁
Where:
Ʃx = the summation of x or (the sum of
the measure)
N = number of the values of x
First example:
80, 80, 83, 84, 85, 87, 88, 89, 90, 94
So from the formula given, let us now try to
analyze and then substitute the given values to
the given formula.
𝑥̅ =
Ʃ𝑥
𝑁
𝑥̅ =
80+80+83+84+85+87+88+89+90+94
10
Hence, the mean grade of the ten students is
86.
Second example:
The five players of basketball team have the
scores of 10, 15, 20, 10, and 25.
Find the mean:
𝑥̅ =
Ʃ𝑥
𝑁
𝑥̅ =
10+15+20+10+25
5
𝑥̅ =
80
5
𝑥̅ = 16
𝑥̅= 86

4. Therefore, the mean score of five players of
basketball is equal to 16.
Do you understand class on how to find the
mean of the given data?
Is there any question?
Okay let us proceed to the second measure of
central tendency.
Median – is the midpoint of the array. The
median will be either a specific value or will fall
between two values.
First example:
Using the same data above.
The math grades of ten students are 85, 80, 88,
83, 87, 89, 84, 80, 94, and 90.
Find the median.
Solution:
To find the median, we need to arrange first the
data in increasing order that is from least to
greatest or vice versa.
80, 80, 83, 84, 85, 87, 88, 89, 90, 94
Since the middle point falls halfway between 85
and 87, so in order to get the median, we need
get the mean 0f these two values.
Median =
85+87
2
Median =
172
2
Median = 86
Therefore, the median of the given data is 86.
Yes, ma’am
No, ma’am

5. Second example:
10, 15, 20, 10, 25
Solution:
Arrange the data in increasing order, from least
to greatest or from greatest to least.
10, 10, 15, 20, 25
Median= 15
Third example:
Using the same formula.
The weights of nine boxing players are recorded
as follows (in pounds).
206,215,305,206,265,265,297,282,301
Now try to solve it in your notebook and then I
will be calling somebody to answer it on the
board.
So do you understand class on how to find the
median of a set of data?
Is there any question?
Okay let us proceed to the next measure of
central tendency.
Mode- it is the value that occurs most often in
the data set. It is the value with the greatest
frequency. A data can have more than one or
none at all. To find the mode for a set of data
we are to consider the following:
Solution:
Arrange first the data in increasing order, from
least to greatest on vice versa.
206, 206, 215, 265, 282, 297, 301, 305
Median = 265
Yes, ma’am
No, ma’am

6. 1.) Select the measure that appears most often
in the set.
2.) If two or more measures appear the same
number of times, then each of these values is a
mode.
3.) If every measure appears the same number
of times, then the set of data has no mode.
First example:
Using the same data above.
80,80,83,84,85,87,88,89,90,94
Since 80 is the value that most often occur in
the given data, therefore 80 is the mode.
Second example:
206,206,215,265,265,282,297,301,305
So now I want you to solve or to get the mode
of the given data.
Very good!
Class, is everything clear?
Do you have question?
D. Values Integration
Class a while ago, we discuss about on how to
measure central tendency of ungrouped data.
From the word central class, we can associate it
with the word center.
How will you define the word center?
Yes,___________
That’s right!
206, 206, 215, 265, 265, 282, 297, 301 305
The modes of the given data are 206 and 265,
since these are the values that most often occur
in the given data.
Yes, Ma’am
None, Ma’am
It is the middle part of everything around us.

7. Now, how about in your real life situation class,
who is the center of your life?
Yes,___________
Another idea?
Yes,___________
Very good!
How about God, did you also make Him as the
center of your life?
Why did you make God as the center of your
life?
Yes,___________
Exactly!
So class, whoever is the center of our life we
should not forget God because He is the source
of everything. Whatever decision or thing we
will make, we should not forget God because
without Him we are nothing.
E. Application
Activity 1
Directions: Find the mean, median, and mode
of the following set of data.
1.) The data below show the score of 20
students in a Biology quiz.
25 33 35 45 34
26 29 35 38 40
45 38 28 29 25
39 32 27 47 45
The center of my life is my family.
The center of my life is my mother.
Yes, ma’am
I always make God as the center of my life
because I know ma’am with god nothing is
impossible.
a.) Mean
x = ∑ 𝑥
N
= 25 + 26 + 45 + 39 + 33 + 29 + 38 + 32 + 35
+ 35 + 28 + 37 + 45 + 38 + 29 + 47 + 34 +
40 + 25 + 45
x = 705 = 35.25
20

8. V. Evaluation
Directions: The data below show the score of
40 students in the 2012 Division Achievement
Test (DAT). Analyze the given data and answer
the questions below.
35 16 28 43 21 17 15 16
20 18 25 22 33 18 32 38
23 32 18 25 35 18 20 22
36 22 17 22 16 23 24 15
15 23 22 20 14 39 22 38
a.) What score is typical to the group of
students?
b.) What score appears to be the median? How
many students fail below that score?
c.) Which score frequently appears?
d.) Find the mean, median and mode.
e.) Describe the data in terms of the mean,
median and mode.
b.) Median = 25, 25, 26, 28, 29, 29, 32, 33, 34, 35,
37, 38, 38, 39, 40, 45, 45, 45, 47
Md = 35 + 35 = 70 = 35
2 2
c. Mode = 45
a.) 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 18, 20,
20, 20, 21, 22, 22, 22, 22, 22, 22, 23, 23, 23, 24, 25,
25, 28, 32, 32, 33, 35, 35, 36, 38, 38, 39, 43
The score that is typical to the group of
students is 22.
b.) A score that appears to be the median is 22
and there are 15 students who got scores below
22.
c.) A score that frequently appears is 22.
d.) The means is 23.95, the median is 22, and
the mode is 22.
e.)

9. VI. Assignment
Directions: In your one-half crosswise, find the
mean, median and mode.
1.) Twelve computer students were given a
typing test and the times (in minutes) to
compute the test were as follow:
8, 12, 15, 14, 19, 21, 24, & 38
2.) A shampoo manufacturerproduces a bottle
with an advertised content of 310 ml. A sample
of 16 bottles yielded the following contents:
297 318 306 300 322 307 312 300
311 303 291 298 315 296 309 311