Mathematics - Senior Secondary 2 - Statistics I

Statistics I

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TERM: 3RD TERM

Week: 1

Class: Senior Secondary School 2
Age: 16 years
Duration: 40 minutes per period (5 periods)
Subject: Mathematics
Topic: Statistics I
Focus: Meaning and computation of mean, median, and mode of ungrouped/discrete data, dispersion concepts (range, variance, standard deviation), presentation of grouped data, and understanding class intervals, class boundaries, and class marks.

 

SPECIFIC OBJECTIVES:

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

  1. Define and compute the mean, median, and mode for ungrouped (discrete) data.
  2. Understand the concept of dispersion and calculate range, variance, and standard deviation for ungrouped data.
  3. Identify and present grouped data figures.
  4. Understand and compute class intervals, class boundaries, and class marks.

 

INSTRUCTIONAL TECHNIQUES:

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

 

INSTRUCTIONAL RESOURCES:

  • Ages of students (for example-based statistics)
  • Poles of different heights (to illustrate variance and standard deviation)
  • Objects and score charts
  • Grouped frequency tables
  • Scientific calculators for calculation exercises

 

PERIOD 1: Introduction to Measures of Central Tendency

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Revises with students the concepts of mean, median, and mode. Uses examples such as ages, heights, or scores of students.

Students recall the definitions and previous knowledge of the mean, median, and mode.

Step 2 - Demonstration of Mean

Demonstrates the computation of the mean using a set of data (e.g., 10 students' ages). Shows manual calculation and calculator usage.

Students practice calculating the mean using the data provided.

Step 3 - Median and Mode

Explains the computation of median and mode for a data set. Demonstrates with examples (e.g., a set of exam scores).

Students calculate the median and mode for a similar set of data.

Step 4 - Guided Practice

Students calculate the mean, median, and mode of their own scores or ages in pairs.

Students work in pairs to calculate the required statistics.

EVALUATION:

  1. What is the formula for calculating the mean?
  2. How do you find the median of a set of data?
  3. What is the mode of the following data set: {2, 4, 6, 6, 7, 7, 7, 9}?

CLASSWORK:

  1. Calculate the mean, median, and mode for the following data: {10, 12, 15, 15, 20, 25}.
  2. Find the mode of the following data set: {9, 11, 12, 12, 15}.
  3. Compute the median of the following data: {5, 7, 8, 9, 10}.

ASSIGNMENT:

  1. Calculate the mean, median, and mode for the data set: {1, 3, 5, 7, 9, 11, 13}.
  2. Explain the difference between mean, median, and mode with examples.

 

PERIOD 2: Understanding Dispersion and Range

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains the concept of dispersion and why it's important. Introduces the range as the simplest measure of dispersion.

Students listen to the explanation and ask questions.

Step 2 - Range

Demonstrates how to compute the range of a data set (e.g., {1, 3, 5, 7, 9}). Formula: Range = Highest value - Lowest value.

Students practice calculating the range of different data sets.

Step 3 - Variance and Standard Deviation

Introduces the formula for variance and standard deviation. Demonstrates the process using a small data set.

Students observe and take notes on the formulas and example calculations.

Step 4 - Guided Practice

Students compute variance and standard deviation for a set of data, working in pairs.

Students perform calculations in pairs under teacher guidance.

EVALUATION:

  1. What is the formula for the range of a data set?
  2. How do you calculate variance and standard deviation?
  3. Why is it important to understand measures of dispersion?

CLASSWORK:

  1. Compute the range, variance, and standard deviation for the following data: {2, 5, 7, 9, 11}.
  2. Calculate the standard deviation for the data set: {1, 3, 5, 7, 9}.

ASSIGNMENT:

  1. Calculate the range and standard deviation for the data set: {3, 6, 9, 12, 15}.
  2. Explain the meaning of variance and why it is used in statistics.

 

PERIOD 3: Presentation of Grouped Data

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains the concept of grouped data and when it's used (large data sets).

Students listen and ask clarifying questions.

Step 2 - Grouped Data Tables

Demonstrates how to present data in grouped frequency tables. Uses an example such as student heights or ages.

Students take notes and prepare their own data sets for practice.

Step 3 - Practice

Students work in groups to create frequency tables from a set of raw data (e.g., test scores).

Students create their own grouped frequency tables in groups.

EVALUATION:

  1. What is the advantage of using grouped data?
  2. How do you construct a grouped frequency table?

CLASSWORK:

  1. Create a grouped frequency table for the following data set: {10, 12, 15, 17, 20, 20, 22, 25, 27, 30}.
  2. Explain how to determine the class interval and frequency in a frequency table.

ASSIGNMENT:

  1. Group the following data into appropriate class intervals: {1, 3, 4, 7, 8, 9, 10, 12, 15, 16, 18}.
  2. Write down the class intervals and frequencies for the following data set: {15, 16, 16, 17, 18, 19, 20, 21}.

 

PERIOD 4: Understanding Class Intervals, Boundaries, and Mid-Values

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Class Intervals

Defines class intervals and how to determine them. Uses an example to explain the concept of class width.

Students listen and follow along with examples.

Step 2 - Class Boundaries

Demonstrates how to calculate class boundaries from class intervals (e.g., 10-20, boundaries: 9.5-20.5).

Students practice calculating class boundaries from sample data.

Step 3 - Mid-Value

Explains how to compute the mid-value of each class interval by averaging the lower and upper boundaries.

Students calculate mid-values for given class intervals.

Step 4 - Practice

Students work on problems involving class intervals, boundaries, and mid-values.

Students work through problems under teacher supervision.

EVALUATION:

  1. How do you determine the class width in a frequency table?
  2. What are class boundaries and how are they calculated?

CLASSWORK:

  1. Determine the class boundaries and mid-values for the class interval 10-20.
  2. Calculate the mid-values for the following intervals: {5-10, 10-15, 15-20}.

ASSIGNMENT:

  1. Calculate the mid-value for the class interval 20-30.
  2. Write the class boundaries for the interval 30-40.

 

PERIOD 5: Recap and Comprehensive Review

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Review

Reviews all topics covered in the week, focusing on mean, median, mode, and dispersion concepts.

Students ask questions and clarify doubts.

Step 2 - Application

Provides a final practice problem involving all aspects (mean, median, mode, dispersion, grouped data).

Students complete the final problem independently.

Step 3 - Wrap-up

Summarizes key concepts and assigns final exercises.

Students note down key points and complete the assignment.

EVALUATION:

  1. Review all concepts: mean, median, mode, range, variance, and standard deviation.

CLASSWORK:

  1. Calculate the mean, median, mode, range, variance, and standard deviation for the following data: {2, 5, 7, 9, 12}.
  2. Create a frequency table for a given data set.

ASSIGNMENT:

  1. Review all the topics covered in the week and prepare for a short quiz on statistics.