Detailed Lesson Plan
Mathematics VIII
I.
Learning Objectives
At the end of the lesson, the students are able to:
a) define mean, median and mode of ungrouped data,
b) examine the data of ungrouped data; and
c) compute data that is given.
II.
Learning Content
Measures of Central Tendency of
Ungrouped Data
Mathematics VIII
Marivel S. Perez
Nicanor M. San Gavriel Jr.
pp. 491-506
Materials:
 PowerPoint presentation for lesson proper.
 Cartolina for motivational activity.
 Printed worksheet for application.
Values/Skills:
 Communication skill
 Collaborative skill
 Active Participation
III.
Learning Experiences (4A’s Method)
Teacher’s Activity
Good morning, class!
Students’ Activity
Good morning, ma’am!
How are you class?
We’re okay, ma’am.
That’s good to hear.
Let’s stand up first for the prayer.
Liza kindly lead the prayer.
Classmate, let us pray.
In the name of the Father…
Alright, before taking our seats,
please pick up the pieces of dirt
under the chair and arrange the
seats properly.
Peverline do we have absentees
today?
None ma’am.
Great. Since everyone’s around
please pass our assignment last
time.
Are all papers in?
Yes, ma’am.
So before we proceed to our next
lesson what is our topic last time?
Yes Shaira?
Ma’am last time we tackle about
parallelism and perpendicularity.
That’s right! Thank you Ms. Shaira.
John Rey Can you tell as what
parallelism is?
Yes ma’am, Parallelism it is the state
of
being
parallel
or
of
corresponding in some way.
Correct! Thank you John Rey.
So two lines are parallel if only if
they are coplanar and they do not
intersect.
Charlotte can you give us an
example.
Yes ma’am. (m ll n)
m
n
That’s awesome Charlotte.
What do you call of a line that
intersect two or more lines?
Ara?
It’s called Transversal Ma’am.
Fabulous!
Let’s talk about Perpendicularity.
Amador can you explain what
Perpendicular is?
Ma’am two lines that intersect to
form right angles are said to be
perpendicular. Line segments and
rays can also be perpendicular.
That is right!
How we can prove that two lines
are perpendicular?
Ms. Jevea?
Ma’am we must show the 3
theorems: 1. If two lines are
perpendicular to each other, then
they form four right angles. 2. If the
angles in a linear pair are
congruent, then the lines
containing their sides are
perpendicular.
That’s awesome. Thank you Ms.
Jevea.
So is that clear class?
Yes, Ma’am
A. Activity
So let’s proceed to our next lesson
but before that let’s have an
activity. Are you familiar of game
called “Four pic One word”
Yes, Ma’am
That’s great so i have here a set of
pictures and all you have to do is to
guess the hidden word behind of
those pictures. So did you get it
class?
Yes, Ma’am.
For the first set of pictures we have
here.
Anyone? Yes Roy?
Sum Ma’am.
That’s right Roy.
Okay for the second set of pictures
we have:
Shaina what is the word?
Middle ma’am.
That’s correct.
Okay for the third set:
Shaan?
Average ma’am
Thank you Shaan.
The last one set:
Jevea?
Frequent.
Thank you Jevea. So we have SUM,
MIDDLE, AVERAGE and FREQUENT.
And let’s use this words in our
another activity. I have here a die
that
every
sides
has
a
correspondent value. The die will
be tossed 7 times to get data.
(the results vary in the draw)
What is the sum of the results?
Jommel?
(according to the results)
So what is the average of the
results? Janel?
(according to the results)
What is the middle value? Liza?
(according to the results)
What is the frequent value? Joyce?
(according to the results)
A. Analysis
Terrific class!
So anyone can tell me what we are
going to discuss today? Eloisa?
Ma’am I think we will talk about
Measures of Central Tendency
That’s right Ms. Eloisa.
We are going to discuss Measures
of Central Tendency of Ungrouped
Data.
A. Abstraction
Before we proceed to our proper
discussion may I present to you the
learning objectives.
Kindly read Sandy.
At the end of the lesson, the
students are able to:
a. define mean, median and
mode of ungrouped data,
b. explain the data of ungrouped
data; and
c. compute data that is given
In statistics, Measures of Central
Tendency is a measurement of
data that indicates where the
middle of the information lies.
What are the 3 measures of central
tendency?
Shaina?
Mean, Median and Mode Ma’am.
Thank you, Shaina.
Vic, what do you mean by mean
Ma’am mean is also known as
average, to find this we should
add all numbers in data and
then dividing by the number of
values in the set. Mean is also
called as arithmetic mean.
Thank you Mr. Vic.
So, if mean is the average, let us
find out how to solve for the
mean. So any one here know
the
formula
for
finding
the
mean? Charlotte?
To get the mean, we use the
formula:
∑𝒙
𝒏
where:
x̅ =
x̅ = mean
∑ = summation of
x = quantities or scores
N = total number of quantities
Superb!
I will show examples, then, let’s
try to find/solve for the mean of
the given data by using the
given formula. Let’s say: 87 88
83 84 85 .
Who wants to try? Lyka?
x̅ =
∑𝒙
𝒏
87+88+83+84+85
x̅ =
5
427
=5
= 85.4
The mean is 85.4
Excellent! Another example.
The score of the learner in his
four written works are
15,19,21,25. What will be his
average score?
Using the formula, can you solve
for the mean. Yes, Shaan?
15+19+21+25
x̅ =
4
80
=4
= 20
The mean is 20.
Thank you Ms. Shaan
Are clear class about on how we
find mean?
That’s right! Using the formula for
mean substitute the given then
divide it to total number of
quantities. Did you get it class?
Yes, Ma’am.
How about Median?
Mr. Betito?
Ma’am median is the value of in the
middle of the data set.
Thank you Mr. Betito
For example; 1 2 3 4 5 what is the
median of this set? Janel?
3 Ma’am.
That’s right!
I have here a given set of numbers.
3, 4, 7, 8, 9, 11
What is/are the middle numbers?
Ms. Liza?
7 and 8 Ma’am.
Terrific!
In this case, we have two values
in the middle. We are just going
to add the number of the cards
and then get the mean of the
two numbers (or divide the sum
into 2) to get the median.What is
the median now? Vemalyn?
7.5 ma’am.
That’s right!
There are steps in getting the
median of the given values.
Kindly read the first one, Roy.
Arrange
in
order
the
numbers/values in the set. (From
least to greatest or greatest to
least).
Thank you Roy.
Lets have an example Find the
median 2,7,5,9,10,13,3
First, arrange the set of values. Let
us arrange them in ascending
order. What comes first and what
follows, Jane?
2, followed by 3, then 5, 7, 9, 10,
and lastly 13.
That’s right
What is median? Yes, Jommel?
7 ma’am.
Thank you Jommel
Kindly state the next step Rachel.
Ma’am if the total number of
elements is an odd number,
therefore, the median is the middle
value of the quantities. If n is an
even number, get the 2 numbers at
the middle. Then, get their mean.
Can you please give us an example
Rachel.
Determine the median of the set of
scores: 15,17,22,14,30,27
What is the first step again? Apply
it to the given.
Yes, Eloi?
Ma’am, First, arrange the set of
values in ascending order.
14,15,17,22,27,30
What values are in the middle,
Mary?
Ma’am , the middle numbers are
17 and 22.
What will you do if there are two
middle numbers and what is the
median?
Yes, Shaira?
Ma’am, Add the two middle
numbers then divide it by 2,
ma’am. Therefore, the median is
19.5.
Do you understand?
Yes, Ma’am
The last measure of central
tendency is the mode.
Okay now, take a look at our
examples on the board and tell
me what does mode mean.
4, 5, 3, 3, 5, 3, 1 (The mode is 3)
28, 25, 32, 28, 17, 28 (The mode is 28)
Based on the given examples, who
can now define what mode is?
Yes, Joyce?
Ma’am Mode is the most occurred
number.
Very good! Mode is the quantity
which occurred most frequently in
a set of data.
A set of data that contains only
one mode is called unimodal.
Therefore, those sets a while ago
are considered unimodal since
they only contain 1 mode. If a set
of data having 1 mode is
unimodal, what do you call a set
of data having 2 modes? Yes,
Gelma?
It is called as Bimodal ma’am
Let us have more examples.
Which set of data has TWO
MODES?
a.9, 11, 16, 6, 7, 17, 18
b.18, 7, 10, 7, 18
c.9, 11, 16, 8, 16
Yes, Vemalyn
Letter C ma’am 9 11 16 8 16
The mode is 16
Mr. Betito which set has no mode
Letter A ma’am
That’s right
Since we are already tackled the 3
measures of central tendency is
there any questions?
None ma’am.
A. Application
Compute the data given.
The Mathematics Department of
Science High School is sending a
contestant to a quiz bee
competition. The teachers
decided to select the contestant
from among the top two
performing students of Section 1.
With very limited data, they
considered only the scores of each
student in 10 quizzes.
The scores are tabulated below:
Quiz Number
1
2
3
4
5
6
7
8
9
Total
Zeny
11
13
5
13
7
10
36
13
9
117
Richard
10
10
12
14
15
9
13
13
12
108
a. Find the Median and Mode of
each students.
b. What is the mean of the scores
of both students?
c. How many scores are above
and below the mean of these
scores?
d. Check once more the
distribution of scores. Which of the
two has a more consistent
performance?
e. Whch of the two students do
you think should be sent to
represent the school in the
completion?
IV.
Evaluation
An printed worksheet will be given to everyone. It is compose of
activity that measuring the learnings of the students. Please get one
whole sheet of paper. Please get one worksheet and pass.
Activity 1. (15 points)
The grades in Mathematics of 10 students are 87, 84, 85, 85, 86, 90, 79,
82, 78 and 76.
a. What is the mean of the 10 students?
b. What is the median?
c. What is the mode?
Activity 2. (5 points each)
V.
1. The number of minutes to commute from school to home as survey
from
randomly chosen high school students: 15, 30, 45, 45, 20, 20,
30, 50, 35, 45.
The individual score of group 1 during a math quiz are 16, 17, 18, 15, 15,
17, 19, 20, 21.
Assignment
A. Find the mean, median and mode of each problem.
1. The ages of 6 teachers in a certain school are given as follows: 20, 25,
23, 24, 21, 20.
2. The sizes of pants sold during Monday in a department store are: 15, 20,
15, 22, 20, 18, 24, 15, 24, 23,
24.
B. Read and study about the Measure of Variability.
Mathematics 8
Marivel S. Perez
Nicanor M. San Gavriel Jr.
pp. 507-521
PREPARED BY:
Josephine Pasobillo