Mathematics - Senior Secondary 1 - Construction of Frequency Polygon of a Given Distribution

Construction of Frequency Polygon of a Given Distribution

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  4. Construction of Frequency Polygon of a Given Distribution

Term: 3rd Term

Week: 11

Class: Senior Secondary School 1

Age: 15 years

Duration: 40 minutes per period

Subject: Mathematics

Topic: Construction of Frequency Polygon of a Given Distribution

 

SPECIFIC OBJECTIVES:

By the end of the lesson, students should be able to:

  1. Define and understand the concept of a frequency polygon.
  2. Construct a frequency polygon from a given frequency distribution.
  3. Interpret the frequency polygon and draw conclusions based on it.
  4. Identify the relationship between frequency polygons and histograms.

 

INSTRUCTIONAL TECHNIQUES:

  • Guided demonstration
  • Question and answer
  • Practice exercises
  • Discussion
  • Use of real-life examples

 

INSTRUCTIONAL MATERIALS:

  • Graph board
  • Graph papers
  • Rulers
  • Pencils and erasers
  • Chalkboard for diagrams
  • Frequency distribution table

 

PERIOD 1 & 2: Introduction to Frequency Polygon

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of a frequency polygon as a graphical representation of a frequency distribution using points connected by straight lines.

Students listen and take notes.

Step 2 - Explaining the Concept

Explains the steps involved in constructing a frequency polygon: 1) Prepare a frequency distribution table. 2) Plot the midpoints of each class interval on the horizontal axis. 3) Plot the corresponding frequency on the vertical axis. 4) Connect the points with straight lines.

Students listen attentively and ask questions.

Step 3 - Frequency Polygon vs Histogram

Compares the frequency polygon with a histogram and explains their similarities and differences.

Students compare the frequency polygon to a histogram and take notes.

Step 4 - Example Construction

Demonstrates the construction of a frequency polygon using a sample frequency distribution. Uses a graph board to plot the points and connect them.

Students observe the demonstration and note the method in their exercise books.

Step 5 - Practice

Provides students with a simple frequency distribution and asks them to plot the points and draw the polygon.

Students plot the points and draw the frequency polygon on graph paper.

NOTE ON BOARD:

  • Frequency polygon construction steps.
  • Key differences between histograms and frequency polygons.

 

EVALUATION (5 exercises):

  1. What is a frequency polygon and how is it constructed?
  2. What is the main difference between a frequency polygon and a histogram?
  3. How do you determine the midpoints of class intervals in a frequency distribution?
  4. Why is the frequency polygon useful in statistics?
  5. What do the points on a frequency polygon represent?

CLASSWORK (5 questions):

  1. Construct a frequency polygon from the following frequency distribution:

Class Interval

Frequency

0-10

5

10-20

8

20-30

12

30-40

6

40-50

3
  1. How do you calculate the midpoints of each class interval?
  2. Explain why connecting the points on the frequency polygon is important.
  3. If you are given a histogram, how can you convert it into a frequency polygon?
  4. Draw the frequency polygon for the distribution above and label the axes.

ASSIGNMENT (5 tasks):

  1. Construct a frequency polygon for the following data:

Class Interval

Frequency

0-5

4

5-10

7

10-15

11

15-20

5

20-25

3
  1. Research real-life examples where frequency polygons are used.
  2. Write a brief explanation of how a frequency polygon helps in understanding statistical data.
  3. Plot a frequency polygon for any given dataset you encounter in your daily life (e.g., temperatures, exam scores).
  4. Find the differences in interpretation between histograms and frequency polygons.

 

PERIOD 3 & 4: Guided Practice and Construction

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Review

Reviews the previous lesson on frequency polygons and addresses any questions from students.

Students ask questions for clarification.

Step 2 - Construction Practice

Guides students through constructing a frequency polygon step-by-step using a different frequency distribution example.

Students follow along and construct their own frequency polygons.

Step 3 - Independent Practice

Provides a different frequency distribution for students to work on independently, ensuring they follow the construction steps.

Students work independently to construct their frequency polygons.

Step 4 - Discuss Results

Reviews the completed frequency polygons and compares them with the expected results. Provides feedback and corrects any errors.

Students discuss their solutions and ask questions on any difficulties they faced.

NOTE ON BOARD:

  • Step-by-step instructions for constructing frequency polygons.
  • Midpoint formula:

 

EVALUATION (5 exercises):

  1. Construct the frequency polygon from the following data:

Class Interval

Frequency

10-20

7

20-30

5

30-40

8

40-50

6

50-60

3
  1. Calculate the midpoints of each class interval.
  2. How can you adjust the scale of the frequency polygon if the data is too spread out?
  3. Explain the role of frequency polygons in displaying data trends.
  4. What are the advantages of using a frequency polygon over other types of graphs?

CLASSWORK (5 questions):

  1. Construct the frequency polygon for the dataset provided.
  2. Why is it important to plot the midpoints accurately when constructing a frequency polygon?
  3. Draw the frequency polygon for the data in the previous classwork.
  4. Discuss how the frequency polygon helps to understand the distribution of data.
  5. How can frequency polygons be used in business or economics?

ASSIGNMENT (5 tasks):

  1. Construct a frequency polygon for any class interval dataset you find online or in your textbook.
  2. Create a frequency polygon to compare two sets of data and interpret the differences.
  3. Write a short report explaining the significance of frequency polygons in statistical analysis.
  4. Create a set of data that could be represented by a frequency polygon, and construct the polygon.
  5. Investigate how frequency polygons are used in various industries (e.g., education, healthcare, finance).

 

PERIOD 5: Conclusion and Review

PRESENTATION:

  • Review the key concepts of frequency polygons and their construction.
  • Discuss common errors students may encounter and clarify doubts.
  • Encourage students to ask any remaining questions.

 

EVALUATION:

  1. Review the students' constructed frequency polygons for accuracy.
  2. Assess the correctness of their classwork and assignments.

Provide feedback on their understanding and areas for improvement.