Lesson Plan: Measures of Position – Quartiles of Ungrouped Data
I. Learning Objective
By the end of the lesson, students should be able to:


Illustrate the measures of position: quartiles of ungrouped data.
Compute and interpret the first quartile (Q1), second quartile (Q2/median),
and third quartile (Q3) in real-life contexts.
II. Subject Matter



Topic: Quartiles of Ungrouped Data
Reference: Grade 10 Mathematics Curriculum Guide
Materials: Whiteboard, markers, projector/slides, sample datasets, activity
sheets
III. Learning Competencies




Define quartiles and explain their significance in statistics.
Differentiate quartiles from other measures of position (median,
percentiles, deciles).
Solve problems involving quartiles of ungrouped data.
Apply quartile concepts to real-life situations (e.g., test scores, survey data).
IV. Procedure
A. Introduction (10 minutes)


Motivation/Hook:
Present a scenario: “Imagine your class took a 20-item quiz. How can we
divide the scores into four equal parts to see who performed below average,
average, and above average?”
Connect to prior knowledge: Review median as the middle value of a dataset.
B. Lesson Proper (25 minutes)
1. Concept Presentation
Define quartiles: values that divide an ordered dataset into four equal
parts.
o Introduce Q1, Q2, Q3: Use data set to present the concept of
Quartile point measure
 Q1 = 25th percentile (lower quartile)
 Q2 = 50th percentile (median)
 Q3 = 75th percentile (upper quartile)
2. Steps in Finding Quartiles (Ungrouped Data)
o
o
)
C. Guided Practice (15 minutes)



Provide another dataset (e.g., students’ ages, quiz scores).
Let students compute Q1, Q2, Q3 in pairs.
Teacher circulates to assist and check computations.
D. Application/Integration (10 minutes)

Ask students: “How can quartiles help us interpret class performance,
income distribution, or survey results?”

Example:
Performance Task: Quartiles of Quiz Scores (Grade 10 – SPARROW)
Situation
The Mathematics teacher of Grade 10 – SPARROW recorded the quiz scores (out of 50 points)
of 30 students in a recent Mathematics assessment. The teacher wants to determine how the
scores are distributed using quartiles to better understand student performance and identify
groups that may need support or enrichment.
Below are the arranged quiz scores from lowest to highest:
Student Quiz Score
1
18
2
20
3
21
4
22
5
24
6
25
7
26
8
27
9
28
10
29
11
30
12
31
13
32
14
33
15
34
16
35
17
36
18
37
19
38
20
39
21
40
22
41
23
42
24
43
25
44
26
45
27
46
28
47
29
48
30
50
Tasks
Part A – Computation
Using the data above, compute the following measures of position:
1. First Quartile (Q₁)
2. Second Quartile (Q₂) or Median
3. Third Quartile (Q₃)
Show your complete solution.
Part B – Interpretation
After computing the quartiles, answer the following:
1. What does the value of Q₁ tell about the performance of the lower-performing students in
Grade 10–SPARROW?
2. Interpret the meaning of Q₂ (Median).
What does this reveal about the typical performance of the class?
3. Interpret Q₃.
What does this tell about the higher-performing students?
4. Based on the quartile values, describe the overall distribution of quiz performance.
5. If the passing score is 30 points, what recommendation would you give to:
o students,
o the Mathematics teacher, and
o the school?
Guide for Writing Interpretation
Use statements such as:





“About 25% of the students scored ____ or below.”
“Half of the students scored ____ or lower.”
“Approximately 75% of students obtained ____ or below.”
“The data suggest that…”
“To improve performance, it is recommended that…”
Challenge Question (Higher-Order Thinking)
If the teacher plans to recognize the Top 25% performers, explain how Q₃ can help identify
students who may qualify for recognition.
E. Assessment (10 minutes)

Short quiz:
1. Define quartiles in your own words.
2. Find Q1, Q2, Q3 of the dataset: 12, 15, 20, 25, 30, 35, 40, 45.
3. Interpret the meaning of Q3 in the dataset above.
V. Assignment


Collect 10 data points from your family or community (e.g., daily expenses,
hours of sleep, number of text messages).
Compute Q1, Q2, Q3 and explain what these values mean in your context.
VI. Values Integration


Emphasize fairness and equality: Quartiles divide data into equal parts,
reminding us of balance and inclusivity in society.
Connect to Filipino values: “Just as quartiles divide data fairly, we should
also strive for fairness and equity in our community.”
This lesson plan is structured for 50–60 minutes and balances theory, practice,
and real-life application.
Prepared by:
Reynaldo P. Javier
Teacher III
Content:
Explanation of grouped data and ungrouped data, along with their differences:
Definitions

Ungrouped Data
o Raw data presented in its original form, without being organized into intervals or
categories.
o Example: The ages of 10 students: 13, 14, 15, 14, 16, 15, 14, 13, 15, 16.
Grouped Data
o Data that has been organized into classes or intervals to make it easier to interpret,
especially when dealing with large datasets.
o Example: Ages of 100 students grouped into intervals:
 13–14 years → 40 students
 15–16 years → 60 students

Differences Between Grouped and Ungrouped Data
Aspect
Form
Usefulness
Computation
Clarity
Example (Test
Scores)
Ungrouped Data
Grouped Data
Values organized into intervals or
Raw values listed individually
categories
Best for small datasets
Best for large datasets
Measures (mean, median, quartiles) are
Measures are estimated using
computed directly from individual values class intervals and frequencies
Can be cluttered if dataset is large
Easier to interpret and analyze
70–79 → 2 students, 80–89 → 3
75, 80, 85, 90, 95
students, 90–99 → 5 students
Summary:



Ungrouped data = raw, individual values.
Grouped data = organized into intervals for easier analysis.
Both are used in statistics, but grouped data is more practical when handling large sets of
information.
Five meaningful problems on Quartiles of Ungrouped Data designed for Grade 10 learners,
each grounded in Philippine contexts to make them relatable and engaging.
Problems on Quartiles of Ungrouped Data (Philippine Context)
Problem 1: Tricycle Fare Survey in Pangasinan
A group of students surveyed 12 tricycle rides in Umingan to know the fare they paid (in pesos):
Data: 15, 20, 18, 25, 22, 20, 30, 18, 25, 28, 20, 22
Task: Compute Q1, Q2, and Q3. Interpret what Q1 means in terms of the lowest 25% of fares.
Problem 2: Rice Prices in Local Market
A teacher asked her students to record the price per kilo of rice in different stalls at the public
market (in pesos):
Data: 42, 40, 38, 45, 50, 48, 44, 46, 39, 41
Task: Find Q2 (median) and explain what it tells about the typical rice price in the market.
Problem 3: Daily Hours of Online Learning
During blended learning, 14 Grade 10 students reported the number of hours they spent online
for schoolwork in one day:
Data: 2, 3, 4, 5, 6, 3, 2, 4, 5, 6, 7, 3, 4, 5
Task: Compute Q1, Q2, and Q3. Interpret Q3 in terms of the top 25% of students’ online study
hours.
Problem 4: Mango Harvest in Zambales
A farmer recorded the number of kilos of mangoes harvested from 10 trees:
Data: 25, 30, 28, 35, 40, 32, 38, 36, 29, 33
Task: Find Q1 and Q3. Explain what Q3 means about the most productive trees.
Problem 5: Barangay Clean-Up Volunteers
In a barangay clean-up drive, the number of hours volunteered by 15 residents were recorded:
Data: 1, 2, 3, 2, 4, 5, 3, 2, 6, 4, 3, 2, 5, 4, 3
Task: Compute Q1, Q2, and Q3. Interpret Q2 as the median number of hours volunteered.
These problems are ungrouped data (raw values), and each connects to everyday Philippine
life—transportation, food prices, education, farming, and community service.