Mathematics - Senior Secondary 1 - Statistics (III) - Grouped data

Statistics (III) - Grouped data

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. Statistics (III) - Grouped data

Term: 3rd Term

Week: 10

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Statistics (III) – Grouped Data

SPECIFIC OBJECTIVES:

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

  1. Construct a frequency distribution table from raw data.
  2. Draw histograms from grouped frequency tables using class boundaries.
  3. Estimate the mode from the histogram.
  4. Interpret statistical data displayed in histogram format.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided practice
  • Hands-on construction
  • Group discussion
  • Visual aids and real-life application

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Graph board
  • Graph papers
  • Rulers, pencils, erasers
  • Sample raw data and frequency tables
  • Printed worksheets

 

PERIOD 1 & 2: Introduction to Histograms and Frequency Tables

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Introduction

Introduces the concept of grouped data and explains how it differs from ungrouped data.

Students listen and respond to questions.

Step 2 – Constructing Frequency Table

Demonstrates how to group raw data and construct a frequency distribution table (using class intervals and tally).

Students observe and construct a sample frequency table.

Step 3 – Explaining Class Boundaries

Explains how class boundaries are derived from class intervals.

Students calculate class boundaries.

Step 4 – Drawing Histogram

Uses an example to draw a histogram from the grouped data using class boundaries and frequency.

Students watch, then replicate the process in their notebooks.

Step 5 – Labeling and Scaling

Teaches how to scale axes and label the histogram appropriately.

Students follow teacher’s instructions and draw labeled histograms.

NOTE ON BOARD:

  • Frequency table includes: Class intervals, Frequency, Cumulative frequency.
  • Histogram: Uses class boundaries on x-axis, frequency on y-axis.
  • No space between bars in a histogram.

 

EVALUATION (5 exercises):

  1. State two differences between a bar chart and a histogram.
  2. Given raw data, group it into class intervals and construct a frequency table.
  3. What are class boundaries and why are they important in drawing histograms?
  4. Draw a histogram from the following data: [Provide simple frequency table].
  5. Label the axes correctly on a histogram.

 

CLASSWORK (5 questions):

  1. Group the following raw scores into class intervals of 0–9, 10–19, ..., 50–59 and create a frequency table.
  2. From the table above, calculate the class boundaries.
  3. Draw a histogram from the frequency table.
  4. What is the modal class in your histogram?
  5. Write the title for your histogram and label the axes.

 

ASSIGNMENT (5 tasks):

  1. Find a set of real-life grouped data (e.g., scores in a test) and represent it in a frequency table.
  2. Draw a histogram from your frequency table.
  3. Write a paragraph explaining the steps you followed.
  4. Explain the difference between grouped data and ungrouped data.
  5. Describe two situations in real life where histograms are useful.

 

PERIOD 3 & 4: Estimating the Mode from a Histogram

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Introduction

Recaps histogram construction and introduces the concept of mode.

Students listen and take notes.

Step 2 – Identify Modal Class

Explains how to identify the modal class from the histogram (class with highest bar).

Students observe and identify modal classes in examples.

Step 3 – Estimating the Mode

Demonstrates how to estimate the mode using the formula:

Students take down the formula and observe worked examples.

 

Where:

  • L = lower boundary of modal class
  • f1 = frequency of modal class
  • f0 = frequency before modal class
  • f2 = frequency after modal class
  • h = class width

 

Step 4 – Guided Calculation

Works through a few examples with the class using actual histograms.  Students follow along and solve in their notebooks.

 

Step 5 – Practice

Gives students new data to create histograms and estimate the mode.  Students draw histogram and estimate the mode using the formula.

NOTE ON BOARD:

  • Mode is estimated using the histogram and the formula.
  • Modal class = class with the highest frequency.

 

EVALUATION (5 exercises):

  1. Identify the modal class from a given histogram.
  2. Estimate the mode using the mode formula.
  3. Explain what each variable in the mode formula represents.
  4. Give two real-life applications of estimating mode.
  5. Why is histogram preferred over bar chart for continuous data?

 

CLASSWORK (5 questions):

  1. From a given grouped frequency table, draw a histogram.
  2. Identify the modal class.
  3. Calculate the mode using the formula.
  4. Label and title your histogram properly.
  5. Write a paragraph explaining your steps.

 

ASSIGNMENT (5 tasks):

  1. Draw a histogram from provided frequency data.
  2. Estimate the mode and show all working.
  3. Write the formula for estimating mode and explain each variable.
  4. Explain why histograms are used in data analysis.
  5. Provide an example of data where histogram estimation of mode is useful.

 

PERIOD 5: Conclusion and Review

PRESENTATION:

  • Recap key concepts: Frequency table, class boundaries, histogram, modal class, mode estimation formula.
  • Solve additional examples on the board.
  • Address any questions and misconceptions.

 

EVALUATION:

  1. Quick oral quiz: “What is the modal class?” “What does ‘h’ represent in the formula?”
  2. Check students’ histograms for accuracy.
  3. Review classwork and assignment responses.

Provide feedback and praise efforts.