Further Mathematics - Senior Secondary 1 - Measure of Dispersion

Measure of Dispersion

Get it on Google Play
Get it on the Apple App Store
  1. Home
  2. Comprehensive Lesson Plan and Notes
  3. Senior Secondary 1
  4. Measure of Dispersion

TERM: 2ND TERM

WEEK 10
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Measure of Dispersion
Focus: Range and Inter-Quartiles

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

  1. Define and calculate the range of a set of data.
  2. Understand the concept of inter-quartiles and calculate them.
  3. Use the range and inter-quartiles to interpret the spread of data.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Practice exercises
  • Use of charts to show measures of dispersion

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts illustrating range and inter-quartiles
  • Flashcards with data sets for practice
  • Worksheets for calculating measures of dispersion

PERIOD 1 & 2: Introduction to Range and Inter-Quartiles

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Range

Explains the concept of range as the difference between the highest and lowest values in a data set. Uses an example to show how to calculate the range.

Students listen and take notes. They ask questions about the calculation process.

Step 2 - Range Calculation

Demonstrates how to calculate the range using a sample data set (e.g., 3, 7, 2, 10). Teacher shows how to subtract the smallest number from the largest (10 - 2 = 8).

Students follow the example, calculating the range of other sets of numbers.

Step 3 - Introduction to Inter-Quartiles

Introduces the concept of inter-quartiles and explains that it represents the range within which the middle 50% of the data falls. Shows how to calculate the first (Q1), second (Q2, median), and third (Q3) quartiles.

Students listen to the explanation and take notes on the process.

Step 4 - Inter-Quartiles Calculation

Demonstrates how to calculate the inter-quartiles by first arranging data in ascending order, then determining the quartiles (Q1, Q2, Q3).

Students follow along, arranging data and calculating quartiles in pairs or groups.

NOTE ON BOARD:

  • Range: Range = Largest value - Smallest value
  • Inter-Quartiles:
    • Q1: 25th percentile
    • Q2 (Median): 50th percentile
    • Q3: 75th percentile

EVALUATION (5 exercises):

  1. What is the range of the data set: 5, 12, 8, 20, 7?
  2. Calculate the range of: 15, 22, 10, 30, 19.
  3. Identify Q1, Q2, and Q3 for the data set: 4, 8, 12, 16, 20, 24.
  4. What does the range tell us about a data set?
  5. Explain the difference between range and inter-quartiles.

CLASSWORK (5 questions):

  1. Find the range of: 10, 25, 14, 18.
  2. Calculate Q1, Q2, and Q3 for: 2, 4, 6, 8, 10, 12.
  3. What is the range of the following data: 5, 10, 15, 20?
  4. Find the inter-quartiles for: 1, 4, 7, 10, 13, 16.
  5. Why do we calculate inter-quartiles?

ASSIGNMENT (5 tasks):

  1. Calculate the range of the data set: 13, 22, 9, 15.
  2. Find the inter-quartiles of: 3, 6, 9, 12, 15, 18, 21.
  3. Explain why range might not give a complete picture of a data set.
  4. Calculate Q1, Q2, and Q3 for: 5, 10, 15, 20, 25.
  5. Given the data set 7, 14, 21, 28, find its range and inter-quartiles.

 

PERIOD 3 & 4: Practice with Range and Inter-Quartiles

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Guided Practice (Range)

Provides several data sets for students to practice calculating the range. Teacher works through examples with the class.

Students calculate the range of data sets individually and ask for assistance when needed.

Step 2 - Guided Practice (Inter-Quartiles)

Teacher walks students through the steps of calculating inter-quartiles for different data sets. Emphasizes arranging data in order before finding quartiles.

Students work in pairs or small groups to calculate the inter-quartiles.

Step 3 - Interpretation

Demonstrates how to interpret the results of the range and inter-quartiles, explaining their significance in analyzing data.

Students discuss their results with peers and share how the range and inter-quartiles help in understanding data.

Step 4 - Independent Practice

Provides independent exercises for students to complete, allowing them to apply what they have learned.

Students complete the exercises on their own, seeking help from the teacher if necessary.

NOTE ON BOARD:

  • Interpreting Results:
    • A smaller range indicates data is more clustered.
    • A larger range indicates data is spread out.
    • Inter-quartiles help understand how data is distributed, especially the middle 50%.

EVALUATION (5 exercises):

  1. Calculate the range of the following data set: 1, 6, 9, 14.
  2. Find Q1, Q2, and Q3 for: 3, 5, 7, 9, 11, 13.
  3. What is the significance of inter-quartiles?
  4. Explain why a large range could be misleading.
  5. Calculate the range for: 4, 8, 12, 16, 20.

CLASSWORK (5 questions):

  1. Calculate the range of: 11, 25, 18, 14.
  2. Find the inter-quartiles for: 2, 4, 6, 8, 10.
  3. What does Q2 represent in a data set?
  4. Calculate Q1, Q2, and Q3 for: 3, 6, 9, 12, 15, 18, 21.
  5. If the range is very high, what can we infer about the data set?

ASSIGNMENT (5 tasks):

  1. Calculate the range of: 20, 25, 15, 30.
  2. Find Q1, Q2, and Q3 for: 10, 20, 30, 40, 50.
  3. Why is it important to know the inter-quartiles of data?
  4. Write a paragraph explaining the difference between range and inter-quartiles.

Given the data set 7, 14, 21, 28, calculate the range and the inter-quartiles.