Lesson Note on Measure of Location II for SS1 (SSS 1)

Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 2nd Term
Week: 9
Age: 15 years
Duration: 45 minutes
Subject: Further Maths
Curriculum Theme: Further Mathematics
Previous Lesson: Measure of Dispersion I.
Topic: MEASURE OF LOCATION
Subject Matter: decile, percentile, quartile

Specific Objectives

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

Cognitive Domain:

• Define deciles, percentiles, and quartiles.
• State the formulas for calculating deciles, percentiles, and quartiles for ungrouped and grouped data.
• Calculate deciles, percentiles, and quartiles from given data sets (ungrouped and grouped).

Affective Domain:

• Appreciate the importance of measures of location in data analysis.
• Value precision in calculating statistical measures.

Psychomotor Domain:

• Apply the knowledge of measures of location to solve related problems.
• Accurately determine deciles, percentiles, and quartiles from various data types.

Social Domain:

• Collaborate with peers to solve problems involving measures of location.
• Share understanding of statistical concepts with classmates.

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.
• Further Mathematics Project 1 for Senior Secondary Schools by Bakare, L.O. et al.

Instructional Materials

The teacher will teach this lesson with the aid of:

• Charts illustrating decile, percentile, and quartile calculations.
• Whiteboard/Chalkboard and markers/chalk.
• Prepared data sets (ungrouped and grouped).

Rationale for the Lesson

This lesson helps pupils understand how data can be divided into specific parts, which is important for interpreting and comparing different data sets. It enables pupils to find specific positions within a data distribution, a skill useful in various fields like economics and public health.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic statistics, including measures of central tendency (mean, median, mode), and how to arrange data in ascending or descending order.

Lesson Content/Board Summary

MEASURES OF LOCATION: DECILES, PERCENTILES, AND QUARTILES

Definition of Measures of Location

Measures of location are statistical values that divide a data set into specific equal parts. They help to understand the position of a value within a data distribution.

Deciles

Deciles are values that divide a data set, arranged in ascending order, into ten equal parts. There are nine deciles, denoted as D1, D2, …, D9.

The formulas for calculating deciles are:

• For Ungrouped Data: The k^th decile, Dk, is the value of the k(N+1)/10^th term, where N is the total number of observations and k = 1, 2, …, 9.
• For Grouped Data: Dk = L + [(k(N/10) – cf_b) / f] * i

Where:

• L = Lower class boundary of the decile class.
• N = Total frequency.
• cf_b = Cumulative frequency of the class before the decile class.
• f = Frequency of the decile class.
• i = Class interval/size.
• k = The specific decile (1, 2, …, 9).

Percentiles

Percentiles are values that divide a data set, arranged in ascending order, into one hundred equal parts. There are ninety-nine percentiles, denoted as P1, P2, …, P99.

The formulas for calculating percentiles are:

• For Ungrouped Data: The k^th percentile, Pk, is the value of the k(N+1)/100^th term, where N is the total number of observations and k = 1, 2, …, 99.
• For Grouped Data: Pk = L + [(k(N/100) – cf_b) / f] * i

Where:

• L = Lower class boundary of the percentile class.
• N = Total frequency.
• cf_b = Cumulative frequency of the class before the percentile class.
• f = Frequency of the percentile class.
• i = Class interval/size.
• k = The specific percentile (1, 2, …, 99).

Quartiles

Quartiles are values that divide a data set, arranged in ascending order, into four equal parts. There are three quartiles, denoted as Q1, Q2, and Q3.

• Q1 (First Quartile) is the lower quartile, dividing the lowest 25% of the data.
• Q2 (Second Quartile) is the median, dividing the data into two equal halves (50%).
• Q3 (Third Quartile) is the upper quartile, dividing the highest 25% of the data.

The formulas for calculating quartiles are:

• For Ungrouped Data: The k^th quartile, Qk, is the value of the k(N+1)/4^th term, where N is the total number of observations and k = 1, 2, 3.
• For Grouped Data: Qk = L + [(k(N/4) – cf_b) / f] * i

Where:

• L = Lower class boundary of the quartile class.
• N = Total frequency.
• cf_b = Cumulative frequency of the class before the quartile class.
• f = Frequency of the quartile class.
• i = Class interval/size.
• k = The specific quartile (1, 2, 3).

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 greets the pupils and reviews the previous lesson on measures of central tendency. The teacher then introduces the new topic by asking pupils if they know how to find specific positions in a list, like the 25th position out of 100. This leads to the concept of dividing data into parts.
Pupils’ Activity: Pupils respond to questions and listen attentively.
Learning Point: Pupils are prepared for the new lesson and connect it to prior knowledge.

Step 2: Definition of Measures of Location

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines measures of location and explains their purpose in dividing data into equal parts. The teacher introduces deciles, percentiles, and quartiles as specific types of these measures.
Pupils’ Activity: Pupils listen, take notes, and ask clarifying questions.
Learning Point: Pupils understand the general concept and types of measures of location.

Step 3: Deciles

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains what deciles are, their number, and their notation. The teacher then presents the formulas for calculating deciles for both ungrouped and grouped data, using a chart to illustrate. A simple example for ungrouped data is worked on the board.
Pupils’ Activity: Pupils observe the chart, copy notes, and follow the example.
Learning Point: Pupils learn the definition and formulas for deciles.

Step 4: Percentiles

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains what percentiles are, their number, and their notation. The teacher presents the formulas for calculating percentiles for both ungrouped and grouped data, relating them to deciles. Another simple example for ungrouped data is worked on the board.
Pupils’ Activity: Pupils pay attention, write notes, and compare the formulas to those of deciles.
Learning Point: Pupils learn the definition and formulas for percentiles.

Step 5: Quartiles

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains what quartiles are (Q1, Q2, Q3) and their significance. The teacher presents the formulas for calculating quartiles for both ungrouped and grouped data, highlighting the relationship between Q2 and the median. An example for ungrouped data is worked on the board.
Pupils’ Activity: Pupils listen, take notes, and ask questions regarding the relationship with the median.
Learning Point: Pupils learn the definition and formulas for quartiles.

Step 6: Worked Examples

Time: 5 minutes
Teaching Skill: Problem Solving/Application
Teacher’s Activity: The teacher presents a more complex problem involving grouped data and guides pupils through the steps of calculating a specific decile, percentile, or quartile, emphasizing the correct application of the formulas and the use of cumulative frequency.
Pupils’ Activity: Pupils actively participate in solving the problem, asking questions, and taking down the steps.
Learning Point: Pupils apply the learned formulas to solve problems involving grouped data.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

1. Define a decile.
2. State the formula for calculating the 3rd quartile (Q3) for ungrouped data.
3. Mention two differences between deciles and percentiles.
4. Explain the meaning of the terms ‘L’ and ‘f’ in the formula for grouped data measures of location.

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 location in data analysis. The teacher gives an assignment for pupils to practice calculating these measures from different data sets.
Pupils’ Activity: Pupils listen and copy the assignment.
Learning Point: Pupils consolidate their learning and receive further practice.

Lesson Keywords

• Decile – A value that divides a data set into ten equal parts.
• Percentile – A value that divides a data set into one hundred equal parts.
• Quartile – A value that divides a data set into four equal parts.
• Ungrouped data – Raw data that has not been organized into classes or categories.
• Grouped data – Data organized into classes or categories with their respective frequencies.
• Cumulative frequency – The running total of frequencies.

Differentiation

For struggling learners, the teacher will provide simplified data sets and additional guided practice, focusing on understanding the concept of position before moving to formulas. Advanced learners will be challenged with problems requiring interpretation of the calculated measures or with real-world application scenarios.

Note for teachers using this lesson plan

Ensure that pupils are comfortable with arranging data in ascending order and calculating cumulative frequencies before introducing the formulas for grouped data. Emphasize the clear distinction between the formulas for ungrouped and grouped data. Provide varied examples to cover different scenarios.