Cumulative Frequency (IV)

Grade 12 · Mathematics

Semester 1 | Period 1 | Week 2

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Subject: Mathematics

Semester: 1

Period: 1

Week: 2

WEEK 2

Class: Grade 11
Age: 16 years
Duration: 40 minutes for 5 periods
Subject: Mathematics
Topic: Cumulative Frequency IV
Focus: Understanding Median, Percentiles, Quartiles, Deciles, and the Calculation of These Measures Using the Formula Method

SPECIFIC OBJECTIVES:

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

  1. Explain the meaning of the median on a cumulative frequency curve.
  2. Define and explain percentiles, quartiles, and deciles.
  3. Calculate the median, quartiles, deciles, and percentiles from grouped data using the formula method.

 

INSTRUCTIONAL TECHNIQUES:

  • Lecture and Explanation
  • Guided Practice
  • Discussion and Q&A
  • Demonstration and Graphing
  • Hands-on Practice

 

INSTRUCTIONAL MATERIALS:

  • Graph board and graph books
  • Ruler and pencil
  • Published charts of cumulative frequency curves
  • Data from previous lessons (capital market, stock market, etc.)

 

PERIOD 1 & 2: Introduction to Median, Percentiles, Quartiles, and Deciles

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Defines the median from a cumulative frequency curve and explains its importance. Introduces the concepts of percentiles, quartiles, and deciles.

Students listen attentively and take notes.

Step 2 - Explanation of Percentiles, Quartiles, and Deciles

Explains each concept in detail:

  • Median: The middle value when data is arranged in ascending order.
  • Percentiles: Values below which a certain percentage of data falls.
  • Quartiles: Divide data into four equal parts.
  • Deciles: Divide data into ten equal parts.

Students ask questions and engage in discussion

Step 3 - Drawing Cumulative Frequency Curve (Ogive)

Guides students to plot cumulative frequency curves using given data and explains how these curves help in finding the median, quartiles, percentiles, and deciles

Students follow the steps and draw cumulative frequency curves on graph paper.

NOTE ON BOARD:

  • Median: The value that separates the data into two equal halves.
  • Percentiles: Divides the data into 100 equal parts.
  • Quartiles: Divides the data into 4 equal parts (Q1, Q2, Q3).
  • Deciles: Divides the data into 10 equal parts.
  • Cumulative Frequency Curve: Use the curve to visually estimate the median, quartiles, and deciles.

EVALUATION (5 Exercises):

  1. What is the median in a cumulative frequency curve?
  2. Define percentiles.
  3. What is the difference between quartiles and deciles?
  4. Explain how to find the median from a cumulative frequency curve.
  5. What is the importance of drawing an ogive in statistics?

 

CLASSWORK (5 Questions):

  1. What does a cumulative frequency curve represent?
  2. How can you estimate the median from an ogive?
  3. Explain how you would use an ogive to find quartiles.
  4. Draw a cumulative frequency curve for the following data set: [2, 4, 6, 8, 10, 12, 14, 16, 18, 20].
  5. How do you interpret the position of the 50th percentile in a cumulative frequency curve?

 

ASSIGNMENT (5 Tasks):

  1. Draw a cumulative frequency curve for a given set of data from the stock market.
  2. Calculate the 90th percentile from the following data set: [5, 10, 15, 20, 25, 30, 35, 40].
  3. What is the first quartile (Q1) of the following data set: [3, 5, 8, 10, 12, 15, 18, 20]?
  4. Calculate the deciles for the data set: [1, 4, 7, 10, 13, 16, 19, 22, 25].
  5. Why is it important to understand percentiles in data analysis?

EVALUATION (5 Exercises):

  1. Calculate the median for the following data set: [1, 2, 3, 4, 5, 6, 7, 8, 9].
  2. Calculate the 25th percentile for the following data set: [10, 20, 30, 40, 50].
  3. Determine the first quartile (Q1) for the data set: [12, 14, 16, 18, 20, 22, 24, 26, 28].
  4. Find the 90th percentile from the following data set: [5, 10, 15, 20, 25, 30].
  5. Calculate the decile for the 7th position in the data set: [3, 6, 9, 12, 15, 18, 21, 24].

 

CLASSWORK (5 Questions):

  1. Find the median for the following data set: [3, 5, 7, 9, 11].
  2. Calculate the 75th percentile for the data set: [1, 2, 3, 4, 5, 6, 7, 8, 9].
  3. Calculate the 10th decile for the data set: [1, 2, 3, 4, 5].
  4. What is the difference between percentiles and quartiles?
  5. How do you calculate the quartiles using the formula method?

 

ASSIGNMENT (5 Tasks):

  1. Calculate the median for the data set: [10, 20, 30, 40, 50, 60, 70, 80, 90].
  2. Find the first quartile (Q1) for the data set: [5, 10, 15, 20, 25, 30, 35, 40, 45, 50].
  3. Determine the 50th percentile for the data set: [1, 3, 5, 7, 9, 11, 13, 15, 17].
  4. Calculate the decile for the 4th position from the data set: [8, 16, 24, 32, 40, 48, 56, 64].
  5. Why is the median a more reliable measure of central tendency than the mean in some situations?