Mathematics - Junior Secondary 3 - Application of measures of central tendency

Application of measures of central tendency

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TERM: 3RD TERM

WEEK 4

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

SPECIFIC OBJECTIVES:

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

  1. Apply the mean, median, mode, and range to analyze data.
  2. Understand the relevance of each measure of central tendency in different data sets.
  3. Compare the mean, median, mode, and range for real-life data.
  4. Interpret results to make informed conclusions from data.
  5. Use the measures to solve practical problems.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Real-life examples
  • Group activities
  • Discussions

INSTRUCTIONAL MATERIALS:

  • Worksheets with data sets
  • Whiteboard and marker
  • Flashcards
  • Calculators (optional)

 

PERIOD 1 & 2: Introduction to Measures of Central Tendency

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces mean, median, mode, and range with simple examples.

Pupils listen and take notes.

Step 2 - Explanation

Explains how to calculate each measure: mean (average), median (middle number), mode (most frequent), and range (difference between highest and lowest).

Pupils ask questions and take notes.

Step 3 - Demonstration

Provides a data set and demonstrates the process of calculating each measure.

Pupils follow the demonstration, solving alongside the teacher.

Step 4 - Practice

Gives pupils a small data set to calculate the mean, median, mode, and range.

Pupils solve the exercise individually or in pairs.

EVALUATION (5 exercises):

  1. Find the mean of: 4, 8, 6, 10.
  2. Find the median of: 3, 7, 5, 9, 2.
  3. Find the mode of: 5, 5, 7, 9, 10.
  4. Find the range of: 2, 6, 8, 3, 7.
  5. Find the mean of: 12, 15, 19, 25, 30.

CLASSWORK (5 questions):

  1. Find the mean of: 1, 3, 5, 7, 9.
  2. Find the median of: 5, 12, 14, 17, 19.
  3. Find the mode of: 10, 12, 12, 14, 16.
  4. Find the range of: 3, 7, 8, 12, 5.
  5. Identify the mode of: 7, 8, 10, 7, 5.

ASSIGNMENT (5 tasks):

  1. Calculate the mean of: 3, 6, 9, 12, 15.
  2. Calculate the median of: 2, 5, 8, 11, 14, 16.
  3. Calculate the mode of: 2, 4, 6, 6, 8, 10.
  4. Calculate the range of: 1, 2, 3, 4, 5.
  5. Create a set of 5 numbers and calculate all measures.

 

PERIOD 3 & 4: Application of Measures of Central Tendency to Analyze Data

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces real-life data scenarios (e.g., sports, population statistics).

Pupils listen and think of examples from their daily lives.

Step 2 - Guided Practice

Works through examples of real-life data, applying measures to analyze the information.

Pupils follow along, providing answers and interpretations.

Step 3 - Group Work

Divides pupils into small groups and gives them data sets to analyze.

Pupils work together to calculate and interpret the measures of central tendency.

Step 4 - Discussion

Facilitates a class-wide discussion on the results of each group's analysis.

Pupils share their results and discuss the conclusions.

EVALUATION (5 exercises):

  1. Calculate the mean of the number of goals scored by players in a match: 4, 2, 5, 1, 3.
  2. Calculate the median age of a group of people: 21, 25, 28, 22, 19.
  3. Calculate the mode for the number of books read by students: 3, 3, 4, 5, 3.
  4. Calculate the range of temperatures recorded in a week: 10°C, 12°C, 18°C, 14°C, 16°C.
  5. Use a data set to calculate the mode, median, and range.

CLASSWORK (5 questions):

  1. Analyze the number of students attending after-school activities: 12, 15, 10, 14, 18.
  2. Calculate the mean weight of 5 children: 45, 50, 48, 51, 49.
  3. Find the median of the heights of 7 students: 152, 160, 165, 170, 175, 180, 185.
  4. Find the mode of test scores: 80, 85, 85, 90, 90, 95.
  5. Calculate the range for monthly rainfall in inches: 4, 5, 6, 7, 9.

ASSIGNMENT (5 tasks):

  1. Create a data set of temperatures for a week and calculate the mean, median, and range.
  2. Analyze the number of pets owned by students in your class and calculate the mode.
  3. Create a set of ages and calculate the median and mode.
  4. Analyze the number of pages read by each student and calculate the mean.
  5. Create your own word problem using central tendency measures.

 

PERIOD 5: Application to Real Life Data

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Discusses the real-life relevance of measures of central tendency (e.g., sales data, population statistics).

Pupils listen and engage in the discussion.

Step 2 - Examples

Shows various data and asks pupils to interpret the measures (mean, median, mode, range).

Pupils answer questions and discuss the interpretation of data.

Step 3 - Exercise

Pupils are given a real-life data set to apply all measures of central tendency.

Pupils solve the exercise individually.

EVALUATION (5 exercises):

  1. Calculate the mean of sales data for the last 5 months: 200, 300, 400, 500, 600.
  2. Calculate the median of ages in a survey: 18, 20, 22, 24, 26.
  3. Find the mode of shoe sizes: 8, 9, 9, 10, 11.
  4. Find the range for the number of customers in a shop on different days: 25, 30, 35, 40, 45.
  5. Use any real-life data set to calculate the mode, median, and range.

CLASSWORK (5 tasks):

  1. Analyze the weekly hours worked by five employees: 40, 42, 45, 40, 50.
  2. Analyze the amount of money spent on groceries for a month: 250, 275, 300, 200, 320.
  3. Calculate the mean score of a class on a test: 60, 70, 80, 90, 85.
  4. Find the median of the number of cars sold in 6 months: 100, 120, 130, 150, 160, 170.
  5. Calculate the range for the number of steps walked in a week: 10,000, 12,000, 15,000, 18,000, 20,000.

ASSIGNMENT (5 tasks):

  1. Find the mean of data for the number of books read in a month by students.
  2. Create a data set for monthly temperature and calculate the mean, median, and range.
  3. Analyze the frequency of grades in a subject and calculate the mode.
  4. Use a set of data on the number of sales to calculate the mean and median.

Create a word problem involving central tendency and solve it.