Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: Second Term
Week: 10
Age: 15 years
Duration: 45 minutes
Subject: Further Maths
Curriculum Theme: Further Mathematics
Previous Lesson: Measure of Dispersion II.
Topic: MEASURE OF DISPERSION
Subject Matter: range of data, interquartile range

Specific Objectives

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

Cognitive Domain:

Define measure of dispersion.
State the formula for calculating the range of a data set.
State the formula for calculating the interquartile range of a data set.

Affective Domain:

Appreciate the importance of measures of dispersion in data analysis.
Show confidence in calculating various measures of dispersion.

Psychomotor Domain:

Calculate the range for a given set of ungrouped data.
Calculate the interquartile range for a given set of ungrouped data.

Work collaboratively with peers to solve problems involving measures of dispersion.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Senior Secondary Schools.
State Unified Scheme of Work for Further Mathematics SSS 1.
New Further Mathematics for Senior Secondary Schools by P.N. Okeke and others.

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts showing examples of dispersion calculations.
Whiteboard/Blackboard and markers/chalk.
Scientific calculators.
Textbooks.

Rationale for the Lesson

This lesson helps pupils understand how data points are spread out, not just their average value. Understanding dispersion is important for making informed decisions and interpreting statistical information in various fields of study and daily life.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of ordering data, finding the median, and basic arithmetic operations.

Lesson Content/Board Summary

MEASURE OF DISPERSION

Introduction to Measure of Dispersion

Measures of dispersion describe how spread out or scattered the data points in a data set are from the central value. They provide information about the variability of the data.

Types of Measures of Dispersion

Common measures of dispersion include:

Range
Interquartile Range
Mean Deviation
Variance
Standard Deviation

Range

The range is the simplest measure of dispersion. It is the difference between the highest and lowest values in a data set.

Formula: Range = Highest Value – Lowest Value

Example: For the data set 5, 12, 8, 15, 3, 10

Highest Value = 15

Lowest Value = 3

Range = 15 – 3 = 12

Quartiles

Quartiles divide an ordered data set into four equal parts. There are three quartiles:

First Quartile (Q1): The value below which 25% of the data falls. It is the median of the lower half of the data.
Second Quartile (Q2): The median of the entire data set. 50% of the data falls below it.
Third Quartile (Q3): The value below which 75% of the data falls. It is the median of the upper half of the data.

Steps to find Quartiles:

Arrange the data in ascending order.
Find the median (Q2) of the entire data set.
Divide the data set into two halves (lower and upper) based on Q2.
Find the median of the lower half to get Q1.
Find the median of the upper half to get Q3.

Interquartile Range (IQR)

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). It measures the spread of the middle 50% of the data.

Formula: IQR = Q3 – Q1

Example: For the data set 3, 5, 8, 10, 12, 15, 18

1. Ordered data: 3, 5, 8, 10, 12, 15, 18

2. Q2 (Median) = 10

3. Lower half: 3, 5, 8

4. Q1 (Median of lower half) = 5

5. Upper half: 12, 15, 18

6. Q3 (Median of upper half) = 15

7. IQR = Q3 – Q1 = 15 – 5 = 10

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher introduces the lesson by asking pupils what they understand by ‘spread’ or ‘scatter’ in data. The teacher explains that while measures of central tendency (mean, median, mode) tell us about the center of data, measures of dispersion tell us how spread out the data is.
Pupils’ Activity: Pupils respond to the teacher’s questions and listen attentively.
Learning Point: Pupils understand the concept of data spread and the need for measures of dispersion.

Step 2: Explanation of Measure of Dispersion

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines measures of dispersion and explains their importance in understanding data variability. The teacher lists common types of measures of dispersion.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarification.
Learning Point: Pupils understand the definition and purpose of measures of dispersion.

Step 3: Explanation of Range

Time: 8 minutes
Teaching Skill: Demonstration/Calculation
Teacher’s Activity: The teacher defines the range, states its formula, and demonstrates how to calculate the range using a simple data set on the board. The teacher provides an example for pupils to try.
Pupils’ Activity: Pupils copy notes, observe the demonstration, and attempt to calculate the range for the given example.
Learning Point: Pupils learn to define and calculate the range of a data set.

Step 4: Explanation of Quartiles

Time: 8 minutes
Teaching Skill: Explanation/Sequencing
Teacher’s Activity: The teacher explains what quartiles are (Q1, Q2, Q3) and the steps involved in finding them, emphasizing the need to order the data first. The teacher uses an example to illustrate finding Q1, Q2, and Q3.
Pupils’ Activity: Pupils listen, ask questions, and follow the steps to find quartiles from the example.
Learning Point: Pupils understand the concept of quartiles and how to locate them in a data set.

Step 5: Explanation of Interquartile Range (IQR)

Time: 8 minutes
Teaching Skill: Derivation/Calculation
Teacher’s Activity: The teacher defines the interquartile range (IQR) and states its formula (IQR = Q3 – Q1). Using the same data set from Step 4, the teacher demonstrates how to calculate the IQR.
Pupils’ Activity: Pupils observe the calculation, take notes, and work through the example.
Learning Point: Pupils learn to define and calculate the interquartile range.

Step 6: Worked Examples

Time: 6 minutes
Teaching Skill: Problem Solving/Application
Teacher’s Activity: The teacher provides a new data set and guides pupils through calculating both the range and the interquartile range. The teacher encourages pupils to work independently or in pairs.
Pupils’ Activity: Pupils solve the given problems, seeking clarification where needed.
Learning Point: Pupils apply their knowledge to solve problems involving range and interquartile range.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

What is a measure of dispersion?
State the formula for calculating the range of a data set.
Given the data set: 10, 2, 7, 15, 3. Calculate its range.
Define the interquartile range.
For the data set: 4, 6, 8, 10, 12, 14, 16. Calculate its interquartile range.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 1 minute
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of measures of dispersion in understanding data variability. The teacher gives pupils homework related to calculating range and interquartile range.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: Pupils consolidate their understanding of measures of dispersion, range, and interquartile range.

Lesson Keywords

Dispersion – The spread or scatter of data points.
Range – The difference between the highest and lowest values in a data set.
Quartile – Values that divide an ordered data set into four equal parts.
Interquartile Range (IQR) – The difference between the third quartile (Q3) and the first quartile (Q1).
Data Set – A collection of numbers or values.

Differentiation

For pupils who grasp concepts quickly, the teacher can introduce more complex data sets or discuss the limitations of range. For pupils who need more support, the teacher will provide additional guided practice with simpler data sets and one-on-one assistance during calculations.

Note for teachers using this lesson plan

Ensure pupils have a good understanding of ordering data and finding the median before introducing quartiles. Encourage the use of calculators for larger data sets. Emphasize the steps clearly on the board for better comprehension.