Further Mathematics - Senior Secondary 1 - Measure of Location

Measure of Location

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TERM: 2ND TERM

WEEK 9

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Measure of Location
Focus: Decile, Percentile, Quartile
SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Define deciles, percentiles, and quartiles.
  2. Understand how to calculate and interpret the measures of location.
  3. Calculate deciles, percentiles, and quartiles from a given data set.
  4. Apply the concepts of deciles, percentiles, and quartiles in real-life scenarios.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Practice exercises
  • Real-life applications and examples

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts showing the calculation of deciles, percentiles, and quartiles
  • Worksheets with data sets for practice
  • Calculators

PERIOD 1 & 2: Introduction to Measures of Location (Decile, Percentile, Quartile)

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of measures of location. Explains the terms decile, percentile, and quartile with examples.

Students listen attentively, take notes, and ask clarifying questions.

Step 2 - Deciles

Explains the concept of deciles, showing how a data set is divided into 10 equal parts. Provides an example to illustrate how to calculate deciles.

Students observe the teacher’s example and work through the process with guidance.

Step 3 - Percentiles

Introduces percentiles, explaining how a data set is divided into 100 equal parts. Provides an example of how to calculate percentiles.

Students participate by solving problems on percentiles.

Step 4 - Quartiles

Explains quartiles, focusing on the first, second (median), and third quartiles, and demonstrates their calculation.

Students work in pairs to calculate quartiles from a given data set.

Step 5 - Real-life Applications

Discusses how deciles, percentiles, and quartiles are used in various fields, such as in determining test scores or analyzing income distribution.

Students share examples of where they might see the application of these measures in real life.

NOTE ON BOARD:

  • Deciles: Divide the data into 10 equal parts.
  • Percentiles: Divide the data into 100 equal parts.
  • Quartiles: Divide the data into 4 equal parts (Q1, Q2 (median), Q3).
  • Formula for Quartiles:
    • Q1 = (1/4)(n+1)th value
    • Q2 (Median) = (1/2)(n+1)th value
    • Q3 = (3/4)(n+1)th value

EVALUATION (5 exercises):

  1. What is the difference between deciles, percentiles, and quartiles?
  2. How many equal parts does a data set get divided into for calculating percentiles?
  3. Define the first quartile (Q1).
  4. Calculate the first decile (D1) from the given data set.
  5. If the 25th percentile is 60, what does it mean about the data?

CLASSWORK (5 questions):

  1. Calculate the 5th percentile for the following data: 10, 20, 30, 40, 50, 60.
  2. Calculate the 3rd quartile for the following data set: 5, 10, 15, 20, 25, 30, 35, 40, 45.
  3. What is the 2nd decile of the data set: 15, 20, 30, 35, 40, 50, 60?
  4. Find the median of the following data: 5, 10, 15, 20, 25, 30, 35, 40.
  5. What does the 80th percentile represent in a data set?

ASSIGNMENT (5 tasks):

  1. Calculate the 10th percentile for the following data: 5, 12, 18, 22, 25, 28, 32.
  2. Calculate the 1st quartile and 3rd quartile for the data set: 8, 12, 15, 18, 22, 25, 28, 30.
  3. Find the decile D4 of the following data: 1, 4, 7, 10, 12, 14, 16, 20, 25, 30.
  4. In a dataset of 100 values, what does the 90th percentile represent?
  5. Research real-life examples where quartiles, percentiles, or deciles are applied, and explain them.

PERIOD 3 & 4: Calculation of Deciles, Percentiles, and Quartiles

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Decile Calculation

Demonstrates how to calculate deciles for a given data set by using the formula for deciles and dividing the data into 10 parts.

Students follow along, using the example given by the teacher to calculate deciles.

Step 2 - Percentile Calculation

Shows how to calculate percentiles using the given formula, explaining how to find specific percentiles in a data set.

Students calculate percentiles with the guidance of the teacher.

Step 3 - Quartile Calculation

Demonstrates how to calculate quartiles, using an example to explain the formula for Q1, Q2, and Q3.

Students work through the steps of calculating quartiles from a data set.

Step 4 - Guided Practice

Provides different data sets for students to practice calculating deciles, percentiles, and quartiles. Encourages collaboration and checking answers.

Students work in groups to practice calculations and compare their results.

NOTE ON BOARD:

  • To calculate deciles, percentiles, and quartiles, arrange the data in ascending order, use the formula provided, and interpret the results.
  • Examples of calculations will be done with the data set: 1, 3, 5, 7, 8, 9, 10, 11, 12, 14.

EVALUATION (5 exercises):

  1. Calculate the 4th decile (D4) for the following data set: 5, 10, 15, 20, 25, 30, 35.
  2. Find the 90th percentile for the data set: 10, 12, 15, 18, 20, 22, 24, 26, 30.
  3. What is the second quartile (Q2) of the following data: 12, 15, 20, 25, 30, 35, 40?
  4. Calculate the 3rd decile (D3) for the data set: 5, 7, 8, 10, 12, 15, 17, 20.
  5. What is the 40th percentile of the following data: 1, 3, 5, 7, 9, 10, 12, 15?

CLASSWORK (5 questions):

  1. Calculate the 6th percentile for the data set: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37.
  2. Find the 1st quartile (Q1) for the following data set: 3, 7, 10, 12, 15, 20, 23, 30.
  3. What is the 8th decile (D8) of the data set: 1, 4, 6, 9, 11, 13, 15, 18, 21?
  4. Determine the median (Q2) for the data set: 2, 4, 6, 8, 10, 12, 14.
  5. Calculate the 50th percentile for the data set: 7, 10, 14, 18, 22, 25, 30, 35.

ASSIGNMENT (5 tasks):

  1. Calculate the 50th percentile for the following data: 1, 5, 9, 13, 17, 21, 25.
  2. Find the 4th quartile (Q4) for the data set: 2, 6, 9, 12, 15, 18, 21.
  3. Research how percentile rankings are used in university admissions and explain.
  4. Calculate the 7th decile (D7) for the data set: 1, 3, 5, 7, 8, 10, 12, 14, 16.
  5. Write a brief report on how quartiles are applied in analyzing student test results.