Mathematics - Junior Secondary 1 - Statistics II - Measures of average

Statistics II - Measures of average

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TERM: 3RD TERM

WEEK 11
Class: Junior Secondary School 1
Age: 12 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Statistics II – Measures of Average
Focus: Arithmetic Mean, Mean, and Mode

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

  1. Define and calculate the arithmetic mean.
  2. Understand and calculate the mean of a given data set.
  3. Identify and calculate the mode of a set of data.
  4. Apply the knowledge of mean and mode to real-life situations.
  5. Compare the arithmetic mean and mode, and understand when to use each in data analysis.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Group discussion
• Drills and exercises
• Real-life application

INSTRUCTIONAL MATERIALS:
• Whiteboard and marker
• Graph paper
• Calculators
• Worksheets with data sets
• Flashcards
• Charts for visual demonstration

 

PERIOD 1 & 2: The Arithmetic Mean (Mean)

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains the concept of the arithmetic mean as a measure of central tendency.

Pupils listen and take notes.

Step 2 - Explanation

Provides a simple data set and demonstrates how to calculate the mean (sum of data values divided by the number of data points).

Pupils observe and take notes on the procedure.

Step 3 - Demonstration

Solves examples on the board, showing step-by-step how to calculate the mean.

Pupils solve similar problems with guidance.

Step 4 - Practice

Pupils are given a data set to calculate the mean.

Pupils calculate the mean of the given data.

NOTE ON BOARD:

  • Formula for calculating the mean:
  • Example: For data set 4, 6, 8, 10, 12:
    Mean=4+6+8+10+125=405=8\text{Mean} = \frac{4 + 6 + 8 + 10 + 12}{5} = \frac{40}{5} = 8

EVALUATION (5 exercises):

  1. Calculate the mean of the data set: 5, 10, 15, 20, 25
  2. Find the mean of the numbers 12, 18, 24, 30, 36.
  3. The data set is 2, 3, 4, 5, 6. What is the mean?
  4. Calculate the mean of 1, 7, 9, 11, 13.
  5. Find the mean of the data set: 14, 16, 18, 20, 22.

CLASSWORK (5 questions):

  1. Find the mean of the numbers: 10, 15, 20, 25, 30.
  2. Calculate the mean of the data set: 4, 8, 12, 16, 20.
  3. What is the mean of 11, 14, 17, 20, 23?
  4. The numbers are 2, 4, 6, 8, 10. What is the mean?
  5. Calculate the mean of the following data set: 3, 5, 7, 9, 11.

ASSIGNMENT (5 tasks):

  1. Calculate the mean of the data set: 3, 7, 10, 12, 15.
  2. Find the mean of the numbers: 4, 9, 14, 19, 24.
  3. A class has the following scores: 55, 60, 65, 70, 75. Find the mean score.
  4. What is the mean of the data set: 10, 20, 30, 40, 50?
  5. Calculate the mean of 5, 8, 12, 15, 18.

 

PERIOD 3 & 4: The Mode

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces the concept of the mode as the most frequent value in a data set.

Pupils listen and take notes.

Step 2 - Explanation

Demonstrates how to identify the mode in a set of data.

Pupils observe and practice identifying modes.

Step 3 - Demonstration

Shows examples of data sets with a clear mode.

Pupils identify modes in given examples.

Step 4 - Practice

Pupils are given a set of data to find the mode.

Pupils identify and calculate the mode.

NOTE ON BOARD:

  • The mode is the number that appears most frequently in a data set.
  • Example: For data set 2, 4, 4, 6, 8, the mode is 4.
  • If no number repeats, the data set has no mode.
  • If multiple numbers repeat the same number of times, the data set is multimodal.

EVALUATION (5 exercises):

  1. What is the mode of the data set: 3, 5, 5, 7, 8?
  2. Find the mode of the numbers: 1, 2, 2, 3, 4.
  3. The data set is 10, 12, 12, 15, 18, 18, 18. What is the mode?
  4. Identify the mode of the following: 2, 4, 6, 8, 10.
  5. What is the mode of the data: 9, 10, 10, 11, 12?

CLASSWORK (5 questions):

  1. Find the mode of the data set: 7, 8, 8, 9, 10.
  2. Identify the mode in the numbers: 5, 10, 10, 15, 20.
  3. What is the mode of: 1, 2, 2, 2, 3, 3, 4?
  4. The data set is 14, 15, 16, 17, 17, 18, 18, 19. What is the mode?
  5. Find the mode in the data set: 8, 9, 9, 10, 10, 10.

ASSIGNMENT (5 tasks):

  1. Identify the mode of the numbers: 3, 5, 7, 7, 8, 9, 10.
  2. What is the mode of the data set: 2, 4, 4, 6, 8, 8?
  3. Find the mode of the following data: 1, 2, 3, 3, 4, 5, 5.
  4. Identify the mode for the numbers: 11, 12, 13, 13, 14.
  5. Create your own data set and find the mode.

 

PERIOD 5: Application to Real Life

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Shows how the mean and mode are applied in real-life situations like sports, population, and finance.

Pupils listen and ask questions.

Step 2 - Examples

Demonstrates real-life scenarios where mean and mode are useful (e.g., calculating average scores, finding the most common shoe size).

Pupils observe and discuss examples.

Step 3 - Drill

Pupils work on real-life application problems.

Pupils calculate and interpret mean and mode in real situations.

EVALUATION (5 questions):

  1. Calculate the mean score for a student who got 80, 85, 90, and 95 in four tests.
  2. Identify the mode of the following: 12, 14, 14, 16, 18, 18.
  3. A company recorded sales of 200, 250, 250, 300, 350. What is the mode of the sales?
  4. If the average score of a class is 70, and the data points are 60, 70, 80, 90, what is the mean?
  5. Calculate the mode of test scores: 85, 90, 90, 95, 95, 100.

CLASSWORK (5 tasks):

  1. The data for the number of people attending a concert each day for 5 days: 200, 250, 250, 300, 350. What is the mode?
  2. A student’s test scores: 55, 65, 70, 75, 75, 80. Find the mode.
  3. Calculate the mean of 45, 50, 55, 60, 65.
  4. A shop records these sales in thousands: 5, 10, 10, 15, 20. What is the mode?
  5. Find the mean of the following data: 14, 18, 22, 26, 30.

ASSIGNMENT (5 tasks):

  1. Use the data on the number of people attending a concert to calculate the mean.
  2. Write a short explanation of when to use the mean and when to use the mode.
  3. Identify the mode in the data: 3, 3, 4, 5, 6, 6, 7.
  4. Create a data set and calculate the mean and mode.

Interpret the mode of the following data set: 12, 15, 15, 18, 18.