Mathematics - Junior Secondary 3 - Measures of central tendency

Measures of central tendency

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TERM: 3RD TERM

WEEK 3
Class: Junior Secondary School 3
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Measures of Central Tendency
Focus: Revision of Mean, Median, Mode, and Range

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

  1. Recall the concepts of mean, median, mode, and range.
  2. Calculate the median of a given data set.
  3. Calculate the mode of a given data set.
  4. Calculate the mean of a given data set.
  5. Calculate the range of a given data set.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Discussion
• Exercises
• Real-life application

INSTRUCTIONAL MATERIALS:
• Whiteboard and marker
• Graph paper
• Worksheets
• Calculator (optional)

PERIOD 1 & 2: Revision of Mean, Median, Mode, and Range

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Revises the concepts of mean, median, mode, and range with examples.

Pupils answer questions and provide examples.

Step 2 - Explanation

Explains the formula for calculating mean, median, mode, and range using a simple data set.

Pupils repeat the definitions and work through examples.

Step 3 - Demonstration

Demonstrates how to calculate the mean, median, mode, and range of a set of numbers.

Pupils follow along and ask questions.

Step 4 - Practice

Gives pupils more examples to practice calculating the measures of central tendency.

Pupils solve the problems independently and ask for help if needed.

NOTE ON BOARD:

  • Mean: Sum of all data values ÷ Number of data values
  • Median: The middle value of an ordered data set
  • Mode: The most frequent value in the data set
  • Range: The difference between the largest and smallest data values

EVALUATION (5 exercises):

  1. Find the mean of the data: 4, 7, 9, 10, 12.
  2. Find the median of the data: 3, 5, 8, 9, 11.
  3. Find the mode of the data: 2, 4, 4, 5, 7.
  4. Find the range of the data: 8, 10, 15, 20, 25.
  5. Calculate the mean of the following: 11, 14, 17, 19, 22.

CLASSWORK (5 questions):

  1. Find the mean of the following: 8, 10, 12, 14, 16.
  2. Find the median of the data: 3, 6, 8, 12, 15.
  3. Find the mode of the data: 5, 5, 7, 8, 10.
  4. Calculate the range of the data: 4, 6, 9, 13, 17.
  5. Write the steps to calculate the mode.

ASSIGNMENT (5 tasks):

  1. Calculate the mean of the following: 12, 15, 18, 20, 25.
  2. Calculate the median of the following: 7, 8, 12, 14, 17.
  3. Find the mode of the following: 1, 2, 2, 4, 4, 4, 5.
  4. Calculate the range of the data: 10, 12, 16, 20, 25.
  5. Find the mean, median, mode, and range of the following data: 3, 5, 8, 10, 12.

 

PERIOD 3 & 4: Calculating the Median, Mode, Mean, and Range

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains the importance of calculating the median, mode, mean, and range in analyzing data.

Pupils listen attentively and take notes.

Step 2 - Explanation

Demonstrates how to find the median, mode, mean, and range for larger data sets.

Pupils practice calculating each measure as the teacher explains.

Step 3 - Practice

Provides students with exercises involving larger data sets.

Pupils work in pairs to solve the exercises.

Step 4 - Class Discussion

Discusses the results of exercises and addresses any difficulties.

Pupils share solutions and discuss any challenges they faced.

NOTE ON BOARD:

  • Example for Median: For the data set 1, 3, 5, 7, 9, the median is 5 (the middle number).
  • Example for Mode: For the data set 2, 2, 4, 5, the mode is 2 (the most frequent number).
  • Example for Mean: For the data set 1, 2, 3, 4, 5, the mean is (1+2+3+4+5)/5 = 3.
  • Example for Range: For the data set 1, 2, 3, 4, 5, the range is 5-1 = 4.

EVALUATION (5 exercises):

  1. Find the median of 11, 14, 19, 21, 25, 27.
  2. Find the mode of 3, 6, 7, 7, 9, 12.
  3. Calculate the mean of 6, 8, 10, 12, 14.
  4. Find the range of 2, 4, 6, 8, 10.
  5. Find the mode of 1, 3, 3, 3, 5.

CLASSWORK (5 questions):

  1. Calculate the mean of the following: 5, 9, 13, 18, 21.
  2. Find the median of the following: 8, 11, 14, 19, 23.
  3. Find the mode of the following: 4, 5, 6, 6, 7, 8.
  4. Calculate the range of 7, 9, 11, 14, 17.
  5. Find the mean of the following data: 2, 6, 8, 10, 12.

ASSIGNMENT (5 tasks):

  1. Calculate the mean of 4, 6, 10, 12, 18.
  2. Find the median of the following data: 9, 11, 14, 18, 22.
  3. Find the mode of the data: 3, 3, 5, 7, 7, 7.
  4. Calculate the range of the data: 6, 9, 13, 17, 21.
  5. Find the mean, median, mode, and range of the following data: 4, 8, 10, 12, 14.

PERIOD 5: Application of Measures of Central Tendency

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains real-life applications of central tendency measures (e.g., analyzing test scores, population data).

Pupils listen and ask questions.

Step 2 - Examples

Provides real-life examples where mean, median, mode, and range are used to analyze data.

Pupils participate in the discussion and share ideas.

Step 3 - Application

Pupils work on exercises where they apply the measures of central tendency to real-life data (e.g., class test scores).

Pupils solve problems individually or in pairs.

EVALUATION (5 exercises):

  1. Calculate the mean of test scores: 45, 56, 78, 88, 92.
  2. Find the median test score from the data: 52, 60, 70, 75, 85.
  3. Find the mode of a set of data representing the number of books read by students: 5, 6, 6, 7, 8.
  4. Calculate the range of data: 20, 25, 30, 35, 40.
  5. Create a word problem using the mean, median, mode, or range.

CLASSWORK (5 tasks):

  1. Analyze the test scores: 80, 85, 90, 92, 100.
  2. Apply the mean formula to this set of numbers: 5, 10, 15, 20, 25.
  3. Compare the test scores using the median.
  4. Use mode to describe the favorite fruit of students: Apple, Banana, Apple, Orange.
  5. Calculate the range of the ages of students: 12, 14, 15, 16, 17.

ASSIGNMENT (5 tasks):

  1. Analyze the number of books read by a group of 5 students: 3, 5, 7, 7, 8.
  2. Write the mean of test scores: 70, 72, 74, 78, 80.
  3. Find the median of ages: 12, 15, 17, 19, 21.
  4. Calculate the range of temperatures recorded in a week: 20°C, 25°C, 30°C, 35°C, 40°C.
  5. Create a word problem based on real-life data and solve it using measures of central tendency.