MARIA AURORA NATIONAL HIGH SCHOOL
SAN JOAQUIN, MARIA AURORA, AURORA, 3202
DETAILED LESSON PLAN ON MEASURES OF POSITION (QUARTILE)
ON UNGROUPED DATA
MATH 10 – QUARTER 4
Content Standard: The learner demonstrates understanding of key concepts of measures of Position.
Performance Standard: The Learner is able to conduct systematically a mini -research applying the different
statistical methods.
I.
II.
III.
LEARNING OBJECTIVE: At the end of the lesson, at least 75% of the class should be able to
(KNOWLEDGE): 1. Determine the quartiles of an ungrouped data.
(SKILLS):
2. Solve quartile value of an ungrouped data.
(ATTITUDE):
3. Appreciate the concept of measures of position in real life situation
SUBJECT MATTER:
A. Topic: Measures of Position (Quartile)
B. Learning Competency: Illustrates the following measures of position: quartiles, deciles and percentiles.
M10SP-IVa-1
C. Reference: Mathematics 10 Learner’s Materials p. 373-377
Mathematics 10 Teacher’s Guide p. 328-332
D. Materials: Visual Aid, Power Point Presentation, Laptop, Projector etc.
E. Values Integrated: Teamwork and Collaboration
PROCEDURE:
TEACHER’S ACTIVITIES
STUDENT’S ACTIVITIES
1. Preparation
A. Prayer
“Before we start our class today, please
stand and let us pray…”
“In the name of the Father . . . Amen”
B. Greetings
“Good afterrnoon class!”
“Good afternoon, mam!”
C. Checking of Cleanliness
“Before you take your sets, please
observe proper alignment of chairs and
see to it that your area is free from any
form of trash or any object not related to
our subject.”
The students will arrange their chairs properly
and clean their place before they take their
seats.
D. Checking of Attendance
“Is there any absent for
today?”
“None mam.”
E. Checking of Assignments
“Do you have any assignments?”
“None mam.”
II. Presentation
A. Awareness
Who can recall about the lesson we discussed last
meeting?
It was all about measures of central tendency.
Then what are the measures of central tendency?
The measures are the mean, median and the mode
of ungrouped data.
The mean is?
The average of the data set.
The middle term of the data.
The most frequent occurring value in the data
How about the median? What is the mode?
B. Activity
I will group you into 4 groups. Count off 1- 4
Group 1 occupy the 1st and 2nd row, group 2 stay in the
3rd and 4th row, group 3 1st row and 2nd row in this
side and group 4 occupy the 3rd row and 4th row in this
side.
I want you to play this game. This game is what we call
“4 pics 1 word”. The mechanics are easy, just use the
scrambled letters to have the right answer. The group
who will get the correct answer will be given 1 point.
The group that has the higher points will get a price. Are
you ready?
MREAUSE
UQALE
WOLER
PISTOION
IDEVID
RETQURA
Yes mam
Okay, what words did you encounter from the activity?
The words are Measure, Position, Divide, Equal,
Lower, Quarter.
So, we have the measure and position, divide and equal,
and lower and quarter.
What do you feel with that activity?
Exciting mam.
Do these words connected to each other?
Some of the words are connected to each other like
Divide and equal
Okay those words are connected to each other because it
is part of our lesson this afternoon..
C. Analysis
So, for this afternoon is all about Measures of Positions
on Quartiles.
At the end of this lesson, you are expected to:
1. Determine the quartiles Q1, Q2, and Q3 of an
ungrouped data.
2. Solve quartile value of an ungrouped data; and
lastly
3. Appreciate the concept of measures of position
in real life situation.
Let’s first define these terms first.
What is measure?
Okay, measure is a standard unit used to
express the size, amount, or degree of something.
Measure for me is all about an amount or degree of
something.
Okay. How about position?
A position class it is all about arranging a particular
position that he/she belong.
For instance, what is your position among the siblings in
your family?
Position for me sir is all about taking an action of
where you belong. It gives us direction.
4th mam.
Now let’s talk about quartile.
What is quartile? Who has an idea?
From the word “quart” we have 4, division by 4. Like in
our quarterly examination, it is divided into 4 quarters,
1st quarter, 2nd quarter.
Now let’s discuss about the quartile. Please read the
definition for quartile
We have 3 quartiles, the lower quartile Q1,
middle quartile or median Q2, and the upper
quartile Q3.
No idea mam.
3rd quarter and 4th quarter
Quartile – the score points which divide a
distribution into four equal parts.
The difference between Q3 and Q1 the
interquartile range.
25%
50%
75%
Q1
100%
Q2
Lower
Quartile
Middle
Quartile
Q3
Upper
Quartile
25% of the data has value ≤ Q1. 50% of
the data has a value ≤ Q2 75% of the data
has a value of ≤ Q3.
We have the formula for getting quartiles.
Qk =
𝒌𝒏
𝟒
Where n is the total number of items in thedistribution.
k the position of the data
REMEMBER!
If the quotient obtained is NOT a whole number,
round to the next larger number
Let’s have an example:
The scores of 7 students in a Mathematics
seatwork are: 7, 4, 3, 6, 7, 4, 8. Find Q1, Q2, and
Q3.
1st step is arranging the data into ascending order:
3, 4, 4, 6, 7, 7, 8
2nd step is to find Q1. Use the formula
Qk =
𝑘𝑛 1(7) 7
=
= = 1.75
4
4
4
or 2
So, we have the 2nd position as the lower
quartile. Q1 is 4.
3rd step is to find Q2. Use the formula
𝑄
2=
2(7) 14
= =3.5 =4
4
4
And the 4th position is the middle quartile. Q2 is 6
4th step is to find Q3. Use the formula
𝑄
3=
3(7) 21
= =5.5 =6
4
4
And lastly, the upper quartile
position. Q3 is 7.
3
4
4
6
7
is the 6th
7
8
Q1
Q2
Q3
Lower Quartile Middle Quartile Upper Quartile
And now it’s your turn. Find Q1, Q2, and Q3.
Find Q1, Q2, and Q3 for the data set 10, 2,9, 15, 23,
30, 8, 17, 25, 28
1st step: 2, 8, 9, 10, 15, 17, 23, 25, 28, 30.
2nd step:
𝑄
1=
1(10) 10
= ==2.5 𝑂𝑅 3
4
4
The value of Q1 is 9.
3rd step:
𝑄
2=
2(10) 20
= =5
4
4
The value of Q2 is 15.
4th step:
𝑄
3=
3(10) 30
= =7.5 𝑂𝑅 8
4
4
The value of Q3 is 25.
2
8
9
10
Lower Quartile
15 17
23
Middle Quartile
Yes mam.
Is the answer correct? Yes or No?
Is there any error in the solution?
None mam.
None mam
The answer is correct! Any questions? Clarifications?
Violent reactions?
D. Abstraction
Measures of positions on quartiles.
As a recap, our lesson this morning is all about?
It is really important for us to know or to study the
measure of position for to be guided at all time. For us
not to be ignorance.
Does measures of position really exist in real life?
Yes mam.
25
28
30
Upper Quartile
Okay! How can we apply it or where can you find it in
the real world?
When we get our grades mam.
We can use it when we get the position of our
grades like the highest score and the lowest score.
So, we can determine what subject we need to give
focus to have a higher grade
How?
.
I will give another scenario for measures of positions.
When your 9 classmates will fall in line, we arrange
them in ascending order, from shortest to tallest.
Q2 mam?
What is the position of the 5th person?
Yes mam.
Are you sure?
Q1 mam.
How about the 3rd person from the shortest to tallest?
Yes mam!
Is that correct? Very good!
Another, game in a basketball. Who are basketball
players here?
Me mam.
4 quarters mam.
How many quarters does the game have?
1st quarter, 2nd quarter, 3rd quarter and 4th quarter.
Yes, very good. A basketball is divided into 4 equal
parts. what are those?
In a quarter, how many minutes does the game have?
Every quarter has 10 mins. So, it is equal to all of
the quarter in the game.
Not really mam.
Very good. So, did you understand the concept of
quartile?
Okay, I will ask questions again to make you recall your
lesson.
What is the positions of the quartile?
We have 3 positions, Lower quartile, middle
quartile and, upper quartile.
It is the median?
Median mam.
In other words, what do you call the middle quartile?
Very good.
E. Application
Using the same group, I want you to choose one
representative each group to pick one envelop
from me. Each envelop has a task to do.
Inside these envelopes there are problems for you
to solve, and also it has a way on how you can
present your work in front. Like dancing, singing
and others.
No mam
Understood?
Okay, in other words you present your work in a Okay mam
creative way given in the envelop.
You have 2-3 mins. to present your work,and
will be graded according to this criteria
Content
Creativity
Presentation
Cooperation
Total
Now,
20%
10%
15%
5%
50%
you start discussing with
yourgroupmates.
You will present by:
1.
RAP
2.
SINGING
3.
DANCING
4.
Reciting a poem
(First group problem)
You are going to know what is the quartiles of
the scores in your mathematicsclass of your 5 friends
including yours. Thescores are 3, 5, 6, 8, 8, 10. Find the
Q1, Q2, and Q3.
Q1 is 5, Q2 is 7, and Q3 is 8.
(After the presentation)
Let’s give the group 5claps
(Second group problem)
Find a way that you can get the values quartiles of
the ages of malnourished children in Brgy San
Joaquin.
7, 9, 9, 10, 11, 12, 13, 15, 15, 16, 16
(After the presentation)
Let’s give the group a 4 claps .
(Third group problem)
You want to know how to easily solve a problem
on quartile. So, you invited a your friend who is a
math genius to give you tips on how to solve quartiles
given a sample problem. Find the quartiles of the
scores of 7 students in mathematics remedial class
5, 5, 6, 7, 8 ,9, 10
Q1 is 9, Q2 is 12, and Q3 is 15.
Q1 is 5, Q2 is 7, and Q3 is 9
(After the presentation)
Let’s give them an 6 claps
(Fourth group problem)
Get the quartiles for the numbers won by a
famous basketball team in the municipality of Maria
Aurora.
20, 20, 25, 45, 50
(After the presentation)
Let’s give this group an 5 clap
Let’s give a clap for everyone for a job welldone.
Q1 is 20, Q2 is 25, and Q3 is 45.
What did you feel in the activity?
We feel excited because we didn’t know what
to do but we make it.
What do you learn with the activity?
We learn that we can also have various
presentation of our solutions in math.
That’s right! In math, we can have presentations not just
solving and answering seat works
I will give you your scores in your presentations.
For group 1, your score is______.
For group 2, your score is .
3rd group, your score
.
And last but not the least, 4th group, your score is .
Let’s give a big round of applause for everyone.
IV.
Assessment
Get ½ lengthwise and answer these following
questions
1. Find the lower quartile and upper quartile of the
data. The number of days taken by each of 11
employees to finish a job were
32
39
27
23
42
35
42
29
46
37
42.
2. Find the quartiles of the problem. A group of
students of JNHS obtained the following scores
in their Statistics quiz:
8
5
4
5
7
3
6
V.
Assignment
Research and study in advance about Measures of
Positions on Deciles
PREPARED BY:
ELOISA O. SOLOMON
Teacher II
NOTED:
Dr. ROLANDO DV. RAMOS
Head Teacher III / ESM Department