The document provides a detailed lesson plan on teaching students about quartiles. It includes objectives, subject matter, procedures, and evaluation. The lesson plan involves illustrating quartiles, calculating specified quartiles of data sets, solving problems involving quartiles, and interpreting quartiles. Example problems are provided to find the Q1, Q2, and Q3 values of data sets. Students practice finding quartiles of individual data and grouped data using formulas. The lesson aims to help students understand what quartiles are and learn the key terms and processes for measuring quartiles.

1. Detailed Lesson Plan in Mathematics
10
I. Objectives
At the end of the lesson, the students will be able to:
 Illustrate quartiles
 Calculate a specified quartile of a set of data
 Solve problems involving quartiles
 Interpret quartiles
II. Subject Matter
Topic: Solving Problems Involving Measures of Position (Quartiles)
References: grade10.modyul.online, mathlibra.com/quartiles
Materials: Power Point presentation
III. Procedure
Teacher’s Activity Student’s Activity
A. Preliminary Activities
Good morning class!
Please all stand and let us pray
(The teacher will call someone to lead the
prayer)
Before you take your seats, please pick up the
pieces of paper under your chair.
Thank you class, you may now take your seats.
Monitor, who’s absent for today?
Very good!
Good morning Ma’am
(The appointed student will lead the prayer)
(The students will pick up the pieces of paper)
(The students will be sitting down.)
No one is absent Ma’am
B. Motivation
Before we start our lesson, let’s have a game.
This game is called “Guess a Word in the
Picture”. Wherein I’ll show you a set of pictures,
then you will guess what it is. Is it clear class?
Okay! So, let’s start. The first set of pictures.
That is right! Next picture.
Yes, Ma’am
MEASURE Ma’am

2. Correct! Next, the third set of pictures.
Very good! Next set, who can answer?
Great! How about the last set of pictures?
Excellent class! You guessed and answered all
the pictures. Give yourself five claps!
POSITION Ma’am
DIVIDE Ma’am
FOUR Ma’am
PARTS Ma’am
C. Presentation
Class, those words have something to do with
our lesson for today. Who can again enumerate
all the words?
Very good! Class, our topic for today is about
Measures of Position. Who wants to read the
definition on the screen? Yes?
Very good! Thank you!
Measures of position are statistical values that
divide a set of data into equal groups.
The most common measures of position are
quartile, decile, and percentile. Today, we will
discuss the quartile.
Now class, when you hear the word quartile,
what comes in your mind?
Okay! Meaning, Quartiles are values that divide
a set of data into four equal parts. Each set of
data has three quartiles. What are they?
Very good! Now, to locate the position of the
quartiles, we used the formula
𝑄 = 𝑖 (
𝑛+1
) th
𝑖 4
Measure, Position, Divide, Four, and Parts.
Measures of position are numerical measures
that are used to describe the standing or
location of an observation relative to the rest of
data.
Four, Ma’am
The Q1 or lower quartile, Q2 or median, Q3 or
upper quartile.

3. Where
i - 1, 2, 3
n - the number of values in the set of data.
So, let’s have example 1.
Find the Q1, Q2, Q3 of the following set of data.
10 2 13 12 12 6 5
The first thing we need to do is to arrange the
data in ascending order. Who wants to arrange
the data in ascending order?
Very good, now let’s find Q1.
𝑄 = 𝑖 (
𝑛+1
) th
𝑖 4
Since we are finding the Q1, what will be the
value of i?
𝑄 = 1
𝑛+1
) th
1 ( 4
Great! How about the value of n?
𝑄 = 1
7+1
) th
1 ( 4
Very good! Now let’s add 7+1. 7+1=?
𝑄 = 1
8
) th
1 (
4
Okay! Now 8 divided by 4 is?
𝑄1 = 1 (2) th
Correct! 1 multiply by 2 is?
𝑄1 = 2th
Exactly! Therefore, the Q1 is located in the 2nd
data from the smallest value. So, what is the
value of Q1?
Very good! Now, let’s find Q2. Since, we are
finding for Q2, our i now is?
𝑄 = 𝑖 (
𝑛+1
) th
𝑖 4
𝑄 = 2 (
𝑛+1
) th
2 4
2 5 6 10 12 12 13
1 Ma’am
7 Ma’am
8 Ma’am
2 Ma’am
2 Ma’am
5 Ma’am
2 Ma’am

4. Very good! Now who can solve for Q2?
Excellent! Q2 is located in the 4th
data. So, what
will be the value of Q2?
Correct! Now, who wants to find Q3?
Very good! Q3 is located in the 6th
data. So, what
will be the value of Q3?
Correct! Do you follow class?
Okay! Now, let’s proceed to Quartile of Grouped
data. The formula we are going to use is
𝑘𝑁
−𝑐𝑓𝑏
𝑄𝑖 = 𝐿𝐵 + ( 4 ) i
𝑓𝑄𝑘
Where:
LB – lower boundary of the kth quartile class
N – total frequency
cfb– cumulative frequency before the quartile
fQk– frequency of the quartile class
i–size of the class interval
k – nth quartile
Now, let’s apply the formula in this example.
Who can read the problem?
Thank you!
We need to find all the unknown in the formula
first before we can solve for Q2 by filling up this
table called the frequency table.
𝑄 = 𝑖 (
𝑛+1
) th
𝑖 4
𝑄 = 2 (
𝑛+1
) th
2 4
𝑄 = 2 (
7+1
) th
2 4
𝑄 = 2 (
8
) th
2 4
𝑄2 = 2 (2) th
𝑄2 = 4th
10 Ma’am
𝑄 = 𝑖 (
𝑛+1
) th
𝑖 4
𝑄 = 3 (
𝑛+1
) th
3 4
𝑄 = 3 (
7+1
) th
3 4
𝑄 = 3 (
8
) th
3 4
𝑄3 = 3 (2) th
𝑄3 = 6th
12 Ma’am
Yes Ma’am
Calculate the Q2of the scores of 50 learners in
mathematics in a 40 item test.

5. Class
interval
(score)
Frequency
(f)
Lower
Boundary
(LB)
Less than
cumulative
frequency
36-40 3
31-35 9
26-30 15
21-25 8
16-20 12
11-15 3
The unknown here is the lower boundary (LB)
and the less than cumulative frequency. The
question is how to fill up the lower boundary?
From the word boundary, what is the boundary
of 36 and 35? So, to get the lower boundary, we
are going to subtract 0.5 on the lower class limit.
Very good! Do you follow class?
Next, let’s solve for cumulative frequency. We
will start in the frequency of lowest score. What
is the lowest score?
Very good! What is the frequency of 11-15?
Correct! Next, we just copy 3 and that is our first
cumulative frequency. Now, we get the next
cumulative frequency by adding 3 to 12 and so
on.
3+12 = ?
15+8 = ?
23+15 = ?
38+9 = ?
47+3 = ?
Very good class! That is how we get the
cumulative frequency.
To check if our answer is correct, the total of
frequency should be the same as the last
cumulative frequency which is 50.
Yes Ma’am
11-15 Ma’am
3 Ma’am
15 Ma’am
23 Ma’am
38 Ma’am
47 Ma’am
50 Ma’am
Class
interval
(score)
Frequency
(f)
Lower
Boundary
(LB)
Less than
cumulative
frequency
36-40 3 35.5 50
31-35 9 30.5 47
26-30 15 25.5 38
21-25 8 20.5 23
16-20 12 15.5 15
11-15 3 10.5 3
Class
interval
(score)
Frequency
(f)
Lower
Boundary
(LB)
Less than
cumulative
frequency
36-40 3 35.5
31-35 9 30.5
26-30 15 25.5
21-25 8 20.5
16-20 12 15.5
11-15 3 10.5

6. Now, how do we get the total of frequency?
That’s right! So, what is the total of frequency?
Are they the same?
Okay! How about the class interval? Based on
the scores, what is the size of class interval?
Very good! Now, we can solve for Q2.
The first thing we need to do is to find the Q2
class or the 𝑘𝑁 in the formula.
4
Since, we are finding Q2, what is the value of k?
2𝑁
=
4
Very good! How about the value of N?
2(50)
=
4
Correct! 2 multiply by 50 is?
100
=
4
Great! Now, 100 divided by 4 is?
That’s right. Next, we are going to get the
unknown in the table.
LB=?i = 5
cfb= ? N = 50
fQk = ?
Now, Let’s find LB. Since the Q2 class is equal
to 25, therefore, it is in between 23 and 38. So,
what will be the value of LB? Is it 25.5 or 20.5?
Okay! The LB is 25.5 because the cumulative
frequency of the scores 26-30 is 24-38. Do you
understand class?
By adding all the frequency Ma’am.
50 Ma’am
Yes Ma’am
5 Ma’am
2 Ma’am
50 Ma’am
100 Ma’am
25 Ma’am
(The students will answer)
Yes Ma’am
Class
interval
Frequency
(f)
Lower
Boundary
(LB)
Less than
cumulative
frequency
36-40 3 35.5 50
31-35 9 30.5 47
26-30 15 25.5 38
21-25 8 20.5 23
16-20 12 15.5 15
11-15 3 10.5 3
N = 50
Class
interval
Frequency
(f)
Lower
Boundary
(LB)
Less than
cumulative
frequency
36-40 3 35.5 50
31-35 9 30.5 47
26-30 15 25.5 38
21-25 8 20.5 23
16-20 12 15.5 15
11-15 3 10.5 3
i = 5 N = 50

7. Okay! How about the value of cfb?
That’s great! How about the value of fQk?
Very good! Now, using the given, we can
compute for Q2. Just substitute the value of the
given. Who wants to solve for Q2?
Very good! Therefore, 50% of the students have
a score less than or equal to 26.15. Do you
understand class
23 Ma’am
15 Ma’am
𝑘𝑁
−𝑐𝑓𝑏
𝑄𝑖 = 𝐿𝐵 + ( 4 ) i
𝑓𝑄𝑘
𝑄 = 25.5 + (
25−23
) 5
2 15
𝑄 = 25.5 + (
2
) 5
2 15
𝑄2 = 25.5 + (0.13) 5
𝑄2 = 25.5 + (0.65)
𝑄2 = 26.15
Yes, Ma’am
D. Generalization
Based from our lesson, what have you learned?
Very good! What is Quartile?
Excellent! What are the three quartiles?
Great! Do you understand?
Ma’am, the common measures of position are
quartile, decile, and percentile.
Quartiles are values that divide a set of data into
four equal parts, Ma’am.
The Q1 or lower quartile, Q2 or median, Q3 or
upper quartile.
Yes Ma’am
IV. Evaluation
On your 1 whole sheet of paper, answer the following
1. Find Q2 and Q3 on the following set of data.
2 4 28 16 22 1 18
2. Calculate the lower quartile Q1 for the following grouped frequency distribution:
Class Interval Frequency
21-25 3
16-20 3
11-15 7
6-10 10
1-5 5

8. V. Assignment
Calculate the Q2 and Q3 for the following grouped frequency distribution:
Class Interval Frequency
46-50 2
41-45 8
31-40 12
26-30 22
21-25 18