Mathematics - Senior Secondary 2 - Cumulative frequency II

Cumulative frequency II

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TERM: 3RD TERM

Week: 6

Class: Senior Secondary School 2
Age: 16 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Cumulative Frequency II
Focus: Cumulative frequency curve (ogive), Plotting of cumulative frequency curve/graph, Definition and calculation of median, quartiles, percentiles, interquartile range, and semi-interquartile range (quartile deviation).

 

SPECIFIC OBJECTIVES:

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

  1. Define and understand cumulative frequency and the concept of the ogive.
  2. Plot cumulative frequency curves (ogives) using class boundaries and cumulative frequency data.
  3. Define median, quartiles, and percentiles.
  4. Use the cumulative frequency curve to find the median, quartiles, interquartile range, and semi-interquartile range.

 

INSTRUCTIONAL TECHNIQUES:

  • Guided demonstration
  • Question and answer
  • Group work
  • Practice exercises
  • Real-life applications (data interpretation)

 

INSTRUCTIONAL MATERIALS:

  • Graph board
  • Graph paper
  • Pencils, rulers
  • Charts with cumulative frequency data
  • Calculator (optional)

 

PERIOD 1 & 2: Introduction to Cumulative Frequency and Ogive

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces cumulative frequency and explains its importance in data analysis. Defines cumulative frequency as the running total of frequencies from a frequency distribution table.

Students listen attentively and take notes.

Step 2 - Ogive Definition

Explains what an ogive is: a graph representing cumulative frequency. Emphasizes that the ogive helps to identify the median, quartiles, and percentiles.

Students ask clarifying questions and participate in discussion.

Step 3 - Plotting Points

Demonstrates how to plot points for the cumulative frequency curve using class boundaries on the x-axis and cumulative frequency on the y-axis.

Students observe the teacher's demonstration, taking notes.

Step 4 - Connecting Points

Shows how to connect the points smoothly with a free-hand curve to form the ogive.

Students practice plotting points and joining them to form the ogive.

NOTE ON BOARD

Definition of cumulative frequency, ogive, and class boundaries. Explanation of how to plot and connect points to form the ogive.

Students copy the notes into their notebooks.

EVALUATION (5 exercises):

  1. Define cumulative frequency.
  2. What is an ogive?
  3. How do you plot points for an ogive?
  4. What is the purpose of using an ogive?
  5. What are class boundaries, and why are they important for plotting an ogive?

CLASSWORK (5 questions):

  1. Plot the cumulative frequency curve for the following data: Class intervals: 0-10, 10-20, 20-30, 30-40; Frequencies: 4, 7, 5, 9.
  2. Describe the purpose of an ogive in statistics.
  3. Identify the class boundaries for the intervals 10-20, 20-30.
  4. Explain why you connect the points with a smooth curve.
  5. What does the steepness of the ogive curve indicate?

ASSIGNMENT (5 tasks):

  1. Research how ogives are used in real-life data analysis (e.g., in economics, weather data).
  2. Plot the cumulative frequency curve for the following data: Class intervals: 5-15, 15-25, 25-35, 35-45; Frequencies: 3, 6, 4, 8.
  3. Write the definition of a cumulative frequency table.
  4. Explain the relationship between cumulative frequency and frequency distribution.
  5. Find and define percentiles, and explain their use in statistics.

 

PERIOD 3 & 4: Finding Median, Quartiles, and Percentiles Using the Ogive

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Median from Ogive

Demonstrates how to find the median from the ogive curve: locate the point where the cumulative frequency curve reaches half the total frequency.

Students observe and take notes.

Step 2 - Quartiles

Explains how to locate Q1 (first quartile) and Q3 (third quartile) from the ogive. Emphasizes finding the 25th and 75th percentiles.

Students practice finding quartiles from the ogive under teacher supervision.

Step 3 - Percentiles

Explains how to determine percentiles using the ogive curve by locating the required percentile point and reading off the value.

Students practice calculating percentiles with the teacher’s assistance.

Step 4 - Interquartile Range

Explains how to calculate the interquartile range (IQR) and semi-interquartile range (quartile deviation) using the ogive curve.

Students follow along and complete the practice exercise with teacher guidance.

NOTE ON BOARD:

  • Median: Find the value corresponding to 50% of total cumulative frequency.
  • Quartiles: Q1 corresponds to 25%, Q3 corresponds to 75%.
  • Percentiles: Find the percentile by determining the cumulative frequency corresponding to the desired percentage.
  • Interquartile Range (IQR): IQR = Q3 - Q1.
  • Semi-Interquartile Range: SIR = (Q3 - Q1) / 2.

EVALUATION (5 exercises):

  1. How do you find the median from an ogive curve?
  2. What are quartiles, and how do you locate them on the ogive curve?
  3. Explain the term "interquartile range."
  4. What is the difference between percentiles and quartiles?
  5. How do you calculate the semi-interquartile range?

CLASSWORK (5 questions):

  1. From the given cumulative frequency curve, determine the median.
  2. From the ogive, find the first and third quartiles.
  3. Calculate the interquartile range for the following data: [use class interval and frequency data].
  4. Find the 80th percentile from the ogive curve.
  5. Determine the semi-interquartile range for the data.

ASSIGNMENT (5 tasks):

  1. Find the median for the following frequency data using an ogive.
  2. Calculate the first and third quartiles for the given cumulative frequency distribution.
  3. Define and explain the purpose of percentiles in data analysis.
  4. Use the ogive to find the 90th percentile.
  5. Explain the importance of using the interquartile range in data analysis.

 

PERIOD 5: Final Practice and Recap

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Recap of Key Concepts

Recaps the key concepts of cumulative frequency, ogives, median, quartiles, percentiles, and interquartile range.

Students review notes and ask questions about areas they find difficult.

Step 2 - Guided Practice

Provides more practice exercises, guiding students through the process of reading data from ogives and calculating the median, quartiles, and percentiles.

Students work on problems independently, seeking help when needed.

Step 3 - Final Assessment

Administers a quick assessment to check students’ understanding of the lesson's objectives.

Students complete the assessment and ask for clarification if necessary.

EVALUATION (Final 5 questions):

  1. How do you find the quartiles from an ogive curve?
  2. What is the formula for calculating the interquartile range?
  3. How do you read the median from the cumulative frequency graph?
  4. What does the steepness of the ogive indicate about the distribution of data?
  5. Why is it important to understand percentiles in data analysis?

CLASSWORK (Final 5 questions):

  1. Plot the ogive for the following data and determine the median.
  2. Calculate the interquartile range from a given frequency table using the ogive.
  3. Find the 25th and 75th percentiles from an ogive.
  4. Explain how percentiles are useful in real-life applications.
  5. Define quartile deviation and explain how to calculate it.

ASSIGNMENT (5 tasks):

  1. Find the semi-interquartile range from the cumulative frequency table provided.
  2. Write a brief explanation of how to calculate percentiles from an ogive.
  3. Solve for the median, quartiles, and interquartile range for a new data set.
  4. Research a practical application of the ogive in business or economics.
  5. Practice plotting the ogive and determining statistical measures for different sets of data.