Further Mathematics - Senior Secondary 1 - Measure of Location - Mean, Mode, Median (For Grouped Data)

Measure of Location - Mean, Mode, Median (For Grouped Data)

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TERM: 2ND TERM

WEEK 8
Class: Senior Secondary School 2
Age: 16 years
Duration: 40 minutes of 4 periods
Subject: Mathematics
Topic: Measure of Location – Mean, Mode, Median (For Grouped Data)
Focus: Introduction to measures of location, calculation of the mean, mode, and median for grouped data.

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

  1. Understand the concepts of mean, mode, and median.
  2. Calculate the mean, mode, and median for grouped data.
  3. Apply the measures of location to interpret data sets in real-life scenarios.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Practice exercises
• Discussion
• Visual aids and real-life connections

INSTRUCTIONAL MATERIALS:
• Whiteboard and markers
• Charts illustrating mean, mode, and median
• Graphs or frequency tables for group data
• Calculators for mean calculations
• Worksheets for practice

PERIOD 1 & 2: Introduction to Measures of Location
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of measures of location. Defines mean, mode, and median. Provides examples from daily life.

Students listen attentively, ask clarifying questions, and engage in discussions.

Step 2 - Explanation of Mean

Explains the concept of mean (average) for grouped data: sum of all values divided by the number of values. Provides examples using a frequency table.

Students observe examples and take notes on how to calculate the mean for grouped data.

Step 3 - Explanation of Mode

Explains the concept of mode as the value that appears most frequently in a data set. Discusses how to identify the mode in grouped data.

Students ask questions and participate in identifying the mode from provided data sets.

Step 4 - Explanation of Median

Introduces the median, explaining it as the middle value in an ordered data set. Demonstrates how to find the median in grouped data.

Students follow along and note down the procedure for finding the median.

EVALUATION (5 exercises):

  1. What is the mean of the numbers: 10, 15, 20, 25, 30?
  2. Identify the mode in the data set: 5, 7, 9, 9, 10.
  3. What is the median of the following data set: 3, 6, 7, 9, 11, 14?
  4. Explain how to calculate the mean for grouped data.
  5. What is the mode in the following grouped data: Frequency: 2, 4, 5, 5, 3, 6?

CLASSWORK (5 questions):

  1. Find the mean of the following numbers: 12, 14, 18, 22, 26.
  2. What is the mode in the data set: 15, 22, 22, 25, 30?
  3. Find the median of the following numbers: 5, 8, 10, 12, 16.
  4. What is the mean of the following data: 20, 30, 40, 50, 60, 70?
  5. Identify the mode in the grouped data: Frequency: 3, 2, 8, 5, 7.

ASSIGNMENT (5 tasks):

  1. Calculate the mean of the following data: 7, 9, 12, 15, 18.
  2. Find the mode in this data: 2, 4, 6, 6, 6, 8, 10.
  3. Determine the median of this data set: 8, 10, 15, 18, 20.
  4. In your own words, explain the difference between the mean, median, and mode.
  5. Provide a real-life example where finding the mean, median, and mode is useful.

PERIOD 3 & 4: Calculation of Mean, Mode, and Median for Grouped Data
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Grouped Data

Introduces grouped data and explains how to calculate mean, mode, and median for such data. Provides a sample frequency table.

Students listen and ask clarifying questions about grouped data.

Step 2 - Calculating the Mean for Grouped Data

Explains how to calculate the mean using a frequency table: Multiply each class mark by its corresponding frequency, sum the products, then divide by the total frequency.

Students take notes and calculate the mean using the example provided.

Step 3 - Mode for Grouped Data

Explains how to identify the modal class (the class with the highest frequency). Shows how to calculate mode for grouped data.

Students participate in identifying the modal class and calculating the mode for the example.

Step 4 - Median for Grouped Data

Explains the process of calculating the median for grouped data, including finding the cumulative frequency.

Students follow along and calculate the median using examples.

 

                                                                                                                                            2. Find the mode for the data set:
Class Interval: 0-10, 10-20, 20-30
Frequency: 3, 5, 7.

         3. Determine the median for the given data:
Class Interval: 10-20, 20-30, 30-40
Frequency: 5, 8, 4.

          4. Calculate the mean for the grouped data:
Class Interval: 5-15, 15-25, 25-35
Frequency: 3, 7, 9.

          5. What is the mode of the following data set:
Class Interval: 1-10, 10-20, 20-30, 30-40
Frequency: 10, 12, 5, 8.

CLASSWORK (5 questions):

  1. Find the mean for the following frequency distribution:
    Class Interval: 5-15, 15-25, 25-35
    Frequency: 4, 6, 8.
  2. Identify the mode from the given data:
    Class Interval: 10-20, 20-30, 30-40
    Frequency: 3, 5, 7.
  3. Find the median for this grouped data:
    Class Interval: 0-10, 10-20, 20-30
    Frequency: 6, 8, 10.
  4. Calculate the mean for the following data:
    Class Interval: 0-5, 5-10, 10-15
    Frequency: 3, 7, 5.
  5. Determine the mode for the grouped data:
    Class Interval: 10-20, 20-30, 30-40
    Frequency: 4, 6, 3.

ASSIGNMENT (5 tasks):

  1. Calculate the mean for the following frequency table:
    Class Interval: 0-10, 10-20, 20-30
    Frequency: 5, 10, 15.
  2. Identify the mode for the following data:
    Class Interval: 10-20, 20-30, 30-40
    Frequency: 7, 8, 6.
  3. Find the median for this grouped data:
    Class Interval: 0-10, 10-20, 20-30
    Frequency: 4, 6, 8.
  4. Provide a real-life situation where the use of the mean, median, and mode would be helpful.
  5. Explain how to find the median for grouped data in your own words.