Cumulative Frequency

Grade 11 · Mathematics

Semester 2 | Period 6 | Week 34

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Subject: Mathematics

Semester: 2

Period: 6

Week: 34

Week 34

Class: Grade 11
Age: 16 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Cumulative Frequency
Focus: Construction of cumulative frequency tables, drawing histograms and frequency polygons, and interpreting them.

 

SPECIFIC OBJECTIVES:

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

  1. Construct cumulative frequency tables, including class intervals, tally, frequencies, and class boundaries.
  2. Draw histograms and frequency polygons based on cumulative frequency data.
  3. Deduce the frequency polygon from the histogram.
  4. Draw frequency polygons using mid-values and frequency.
  5. Review and apply these skills in various classwork exercises.

 

INSTRUCTIONAL TECHNIQUES:

  • Direct instruction
  • Guided practice
  • Discussion
  • Hands-on activities
  • Peer learning

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Cumulative frequency curve chart
  • Graph board
  • Graph books
  • Pencils
  • Flashcards with data sets
  • A sample table of class intervals

 

PERIOD 1 & 2: Construction of Cumulative Frequency Table

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of cumulative frequency and explains the importance of class intervals, tally marks, frequencies, and class boundaries.

Students listen attentively and ask clarifying questions.

Step 2 - Data Collection

Teacher suggests 30 quantitative values less than 100 and writes them on the board. Students are asked to suggest additional values to complete the data set.

Students suggest values, and the teacher writes them on the board.

Step 3 - Grouping Data

Teacher demonstrates how to construct a grouped frequency table with class intervals, tally marks, and frequencies.

Students observe and copy the data into their notebooks, working with the class to organize the data into intervals.

Step 4 - Cumulative Frequency

Teacher demonstrates how to calculate cumulative frequency and construct the cumulative frequency table, including class boundaries.

Students practice under the teacher’s supervision, calculating cumulative frequency and identifying class boundaries.

NOTE ON BOARD:

  1. Grouped Frequency Table Example
  2. Cumulative Frequency Table: Includes tally marks, frequencies, cumulative frequencies, and class boundaries.

 

EVALUATION (5 exercises):

  1. What are the class intervals used in constructing a cumulative frequency table?
  2. How do you calculate cumulative frequency from a frequency table?
  3. Define class boundaries and explain their importance.
  4. What is the purpose of tally marks in a frequency table?
  5. How would you find the cumulative frequency for a class interval?

 

CLASSWORK (5 questions):

  1. Construct a grouped frequency table using the following data: 5, 8, 12, 15, 17, 22, 25, 30, 32, 34, 38, 42, 45, 47, 50, 52, 55, 58, 60, 62, 65, 67, 70, 72, 75, 77, 80, 82, 85, 88.
  2. Calculate the cumulative frequency for the grouped table.
  3. Find the class boundaries for the data.
  4. Why do we use class boundaries in cumulative frequency tables?
  5. How can you check for accuracy when constructing a cumulative frequency table?

 

ASSIGNMENT (5 tasks):

  1. Collect 20 random data points less than 100 and construct a frequency table.
  2. Calculate the cumulative frequency for the table and find the class boundaries.
  3. Explain in your own words why cumulative frequency is important for data analysis.
  4. Write down the differences between a frequency table and a cumulative frequency table.
  5. Research how cumulative frequency is used in real-life data collection.

 

PERIOD 3 & 4: Drawing Histogram and Frequency Polygon

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains how to construct a histogram from a cumulative frequency table, highlighting the importance of choosing the correct scale and plotting bars for each class interval.

Students listen attentively and take notes on the procedure for drawing histograms.

Step 2 - Histogram Example

Teacher draws an example of a histogram based on the cumulative frequency data provided, using the graph board.

Students follow along with the teacher, drawing their histograms in their notebooks.

Step 3 - Frequency Polygon

Demonstrates how to convert the histogram into a frequency polygon by connecting the midpoints of the top of the bars.

Students observe and practice drawing a frequency polygon based on the histogram.

Step 4 - Practice

Provides students with the cumulative frequency table to draw histograms and frequency polygons independently.

Students work individually or in pairs to complete the task.

NOTE ON BOARD:

  1. Cumulative Frequency Table and Graphs
  2. Frequency Polygon: Midpoint = (lower class boundary + upper class boundary) ÷ 2
  3. Steps to plot the frequency polygon.

 

EVALUATION (5 exercises):

  1. Draw a histogram for the following cumulative frequency table.
  2. Convert a histogram into a frequency polygon.
  3. What is the purpose of drawing a frequency polygon?
  4. How do the shapes of histograms and frequency polygons help in data interpretation?
  5. Explain how to find the midpoint for a frequency polygon.

 

CLASSWORK (5 questions):

  1. Construct a histogram for the following data:
    • Class Interval: 0-10, 10-20, 20-30, 30-40, 40-50
    • Cumulative Frequency: 5, 12, 18, 23, 30
  2. Draw a frequency polygon for the same data.
  3. What do you observe about the shape of the frequency polygon?
  4. How would you interpret the data from the histogram?
  5. Explain the difference between a histogram and a frequency polygon.

 

ASSIGNMENT (5 tasks):

  1. Draw a histogram and frequency polygon for the following data:
    • Class Interval: 0-5, 5-10, 10-15, 15-20, 20-25
    • Cumulative Frequency: 2, 7, 12, 15, 20
  2. Explain how a frequency polygon helps in identifying trends in data.
  3. What would the graph look like if the data had a normal distribution?
  4. Construct a frequency polygon using the midpoints for the following data.
  5. Research an example of how histograms and frequency polygons are used in real-life statistics.

 

PERIOD 5: Review and Application

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Review

Reviews the process of constructing a cumulative frequency table, drawing histograms, and frequency polygons.

Students ask clarifying questions and review their notes.

Step 2 - Practice

Engages students in various classwork exercises involving the creation of cumulative frequency tables, histograms, and frequency polygons.

Students work on practice exercises individually and in pairs, seeking feedback from the teacher.

Step 3 - Recap

Recaps key points and addresses any lingering questions or difficulties.

Students actively engage in the discussion and share insights.

EVALUATION (5 exercises):

  1. Construct a cumulative frequency table from the given data.
  2. Draw a histogram and frequency polygon from the cumulative frequency table.
  3. Discuss the differences between cumulative frequency tables and frequency polygons.
  4. What is the role of histograms in data analysis?
  5. How can cumulative frequency tables be used to summarize data efficiently?

CLASSWORK (5 questions):

  1. Create a frequency table from the following data: 8, 9, 15, 17, 18, 22, 26, 30, 35, 38, 40, 42, 45, 48.
  2. Draw a histogram for the frequency table.
  3. Convert the histogram into a frequency polygon.
  4. Explain the importance of cumulative frequency in interpreting data.
  5. How can you improve the accuracy of a cumulative frequency curve?

 

ASSIGNMENT (5 tasks):

  1. Create a cumulative frequency table and histogram for your own dataset.
  2. Construct a frequency polygon from your histogram.
  3. Explain the use of cumulative frequency in understanding trends in data.
  4. Why is it important to know how to construct and interpret histograms and frequency polygons?
  5. Research how cumulative frequency and frequency polygons are used in various industries (e.g., business, health).