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 11
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Measure of Dispersion
Focus: Mean Deviation, Standard Deviation, Coefficient of Variation
SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Understand and calculate the mean deviation of a data set.
  2. Compute the standard deviation for a data set.
  3. Calculate the coefficient of variation and understand its significance.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Group discussion
  • Practice exercises
  • Real-life application of measures of dispersion

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts illustrating measures of dispersion
  • Flashcards with examples of data sets for calculation
  • Calculators for practice
  • Worksheets for exercises

PERIOD 1 & 2: Introduction to Measures of Dispersion
PRESENTATION:

         4. What is the significance of the coefficient of variation in comparing two data sets?

         5. What does a larger standard deviation indicate about a data set?

CLASSWORK (5 questions):

  1. Calculate the mean deviation for the data set: [3, 5, 8, 10, 15].
  2. Find the standard deviation for the data set: [10, 20, 30, 40].
  3. Calculate the coefficient of variation for a data set with a mean of 50 and a standard deviation of 10.
  4. What is the relationship between standard deviation and variance?
  5. For which type of data would the coefficient of variation be most useful?

ASSIGNMENT (5 tasks):

  1. Find the mean deviation for the data set: [5, 7, 9, 14, 16].
  2. Calculate the standard deviation for the data set: [4, 6, 8, 10, 12].
  3. Compute the coefficient of variation for a data set with a mean of 30 and a standard deviation of 8.
  4. Identify one real-life application where mean deviation is used.
  5. Find the standard deviation of the following data set: [18, 25, 32, 40, 50].

PERIOD 3 & 4: Application and Practice
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Review of Previous Work

Recaps the calculations of mean deviation, standard deviation, and coefficient of variation. Reviews any common errors from the previous periods.

Students review their notes and ask for clarification on any points they found difficult.

Step 2 - Guided Practice

Provides more complex data sets for students to calculate the measures of dispersion. Demonstrates how to work through problems that involve multiple data sets.

Students work in pairs or groups to calculate the measures of dispersion for the given data sets.

Step 3 - Independent Practice

Assigns additional data sets for students to calculate the mean deviation, standard deviation, and coefficient of variation on their own.

Students work independently, using calculators and their notes to complete the task.

Step 4 - Real-life Connections

Provides examples of how measures of dispersion are used in various fields, such as economics, quality control, and research. Discusses the importance of understanding dispersion in decision-making.

Students participate in the discussion and suggest other fields where measures of dispersion could be applied.

NOTE ON BOARD:

  • Mean Deviation: Helps to understand how spread out the data is from the mean.
  • Standard Deviation: Indicates how much individual data points differ from the mean.
  • Coefficient of Variation: Useful for comparing the variability of different data sets, especially when they have different means.

EVALUATION (5 exercises):

  1. Calculate the mean deviation for the data set: [4, 8, 12, 15, 18].
  2. Compute the standard deviation for the data set: [3, 6, 9, 12, 15].
  3. Calculate the coefficient of variation for a data set with a mean of 25 and a standard deviation of 7.
  4. Compare the dispersion of two data sets using their standard deviations.
  5. Explain how a high coefficient of variation affects decision-making.

CLASSWORK (5 questions):

  1. Find the mean deviation for the data set: [2, 5, 7, 8, 10].
  2. Calculate the standard deviation for the data set: [5, 8, 12, 14].
  3. Compute the coefficient of variation for a data set with a mean of 15 and a standard deviation of 4.
  4. What is the impact of a lower standard deviation on the data set?
  5. How do you interpret a coefficient of variation of 50%?

ASSIGNMENT (5 tasks):

  1. Calculate the mean deviation for the data set: [9, 10, 15, 20, 25].
  2. Find the standard deviation for the data set: [12, 15, 18, 22].
  3. Compute the coefficient of variation for a data set with a mean of 40 and a standard deviation of 12.
  4. Describe an industry or field where the coefficient of variation is essential for analysis.
  5. Provide an example where standard deviation might be more useful than mean deviation.