Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 3rd Term
Week: 9
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Statistics.
Topic: STATISTICS (III) GROUPED DATA
Subject Matter: Drawing histogram from grouped data, Estimation of mode from histogram, Constructing grouped frequency table and using class boundaries.

Specific Objectives

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

Cognitive Domain:

Define grouped data and class boundaries.
Explain the steps involved in constructing a grouped frequency table.
Describe how to draw a histogram from grouped data.
Explain the method of estimating the mode from a histogram.

Affective Domain:

Appreciate the importance of representing statistical data graphically.
Participate actively in class discussions and practical activities.
Develop an interest in analyzing and interpreting grouped data.

Psychomotor Domain:

Construct a grouped frequency table from a given set of data.
Draw an accurate histogram for grouped data using class boundaries.
Estimate the mode of a grouped data set from a constructed histogram.

Work collaboratively with peers to solve statistical problems.
Communicate their understanding of statistical concepts clearly.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Mathematics (Senior Secondary Education)
State Unified Scheme of Work for Senior Secondary School Mathematics
New General Mathematics for Senior Secondary Schools 1 by J.B. Channon, et al.

Instructional Materials

The teacher will teach this lesson with the aid of:

Graph board
Graph papers
Ruler
Pencil
Eraser
Textbook

Rationale for the Lesson

This lesson helps pupils understand how to organize and visualize large sets of data, making it easier to interpret. Learning to draw histograms and estimate the mode from them helps pupils make sense of real-world data in various fields like economics and science.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic statistics, including ungrouped data, frequency tables, and basic graphical representations like bar charts.

Lesson Content/Board Summary

STATISTICS (III) GROUPED DATA

1. Grouped Frequency Table and Class Boundaries

Grouped data is data organized into classes or intervals. A grouped frequency table shows the frequency of observations falling into each class interval.

The following are steps to construct a grouped frequency table:

Determine the range of the data (highest value – lowest value).
Decide on the number of classes (usually between 5 and 15).
Calculate the class interval (range / number of classes).
Set up class limits for each interval.
Determine class boundaries: For a class interval a-b, the lower class boundary is (a + previous upper class limit)/2 and the upper class boundary is (b + next lower class limit)/2. Alternatively, subtract 0.5 from the lower class limit and add 0.5 to the upper class limit (for whole numbers).
Tally the data into the appropriate class intervals.
Count the tallies to find the frequency for each class.

2. Drawing Histogram from Grouped Data

A histogram is a graphical representation of grouped data where the frequency of each class is represented by the height of a bar. The bars are adjacent, indicating continuous data.

The following are steps to draw a histogram:

Construct a grouped frequency table with class boundaries.
Draw a horizontal axis (x-axis) for class boundaries and a vertical axis (y-axis) for frequency.
Label the x-axis with the class boundaries.
Label the y-axis with appropriate frequency scales.
Draw rectangular bars for each class interval. The width of each bar extends from the lower class boundary to the upper class boundary, and its height corresponds to the frequency of that class.
Ensure there are no gaps between the bars.

3. Estimation of Mode from Histogram

The mode for grouped data is the class with the highest frequency (modal class). From a histogram, the mode can be estimated graphically.

The following are steps to estimate the mode from a histogram:

Identify the modal class (the bar with the greatest height).
From the top-right corner of the modal bar, draw a straight line to the top-right corner of the preceding bar.
From the top-left corner of the modal bar, draw a straight line to the top-left corner of the succeeding bar.
The x-coordinate of the intersection point of these two lines represents the estimated mode.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction/Recall
Teacher’s Activity: The teacher greets the pupils and asks them to recall what they learned about ungrouped data and frequency tables in previous lessons. The teacher then introduces the topic of grouped data and its representation.
Pupils’ Activity: Pupils respond to questions about previous lessons and listen attentively to the introduction.
Learning Point: Pupils recall prior knowledge and are introduced to the new topic.

Step 2: Constructing Grouped Frequency Table

Time: 10 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains what grouped data is and guides pupils through the steps of constructing a grouped frequency table from a given raw data set, emphasizing the calculation of class intervals and class boundaries. The teacher works through an example on the board.
Pupils’ Activity: Pupils follow the teacher’s explanation, ask questions for clarification, and copy the example.
Learning Point: Pupils learn how to organize raw data into a grouped frequency table.

Step 3: Understanding Class Boundaries

Time: 5 minutes
Teaching Skill: Clarification/Explanation
Teacher’s Activity: The teacher specifically focuses on the concept and importance of class boundaries for continuous data representation, showing how to convert class limits to class boundaries to ensure continuous bars in a histogram.
Pupils’ Activity: Pupils observe and understand the method of determining class boundaries.
Learning Point: Pupils understand the role of class boundaries in representing continuous data.

Step 4: Drawing Histogram from Grouped Data

Time: 10 minutes
Teaching Skill: Demonstration/Guided Practice
Teacher’s Activity: Using the grouped frequency table constructed in Step 2 (with class boundaries), the teacher demonstrates on the graph board how to draw a histogram, ensuring correct labeling of axes and proper representation of frequencies and class boundaries. The teacher emphasizes that the bars must be adjacent.
Pupils’ Activity: Pupils observe the demonstration and begin to practice drawing histograms on their graph papers.
Learning Point: Pupils learn the practical steps of drawing a histogram.

Step 5: Estimating Mode from Histogram

Time: 5 minutes
Teaching Skill: Demonstration/Illustration
Teacher’s Activity: The teacher demonstrates on the drawn histogram how to estimate the mode by identifying the modal class and drawing the necessary lines to find the intersection point. The teacher explains how to read the estimated mode from the x-axis.
Pupils’ Activity: Pupils observe the demonstration and try to replicate the process on their own histograms.
Learning Point: Pupils learn how to graphically estimate the mode from a histogram.

Step 6: Class Activity/Practice

Time: 5 minutes
Teaching Skill: Application/Observation
Teacher’s Activity: The teacher provides a simple grouped frequency table and asks pupils to quickly draw a histogram and estimate the mode. The teacher moves around the class to observe and assist pupils.
Pupils’ Activity: Pupils attempt to draw a histogram and estimate the mode individually or in pairs.
Learning Point: Pupils apply the learned concepts in a practical exercise.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

Define grouped data.
List three steps involved in constructing a grouped frequency table.
Explain how to determine class boundaries for grouped data.
Describe how to estimate the mode from a histogram.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of grouped data, histograms, and mode estimation. The teacher gives pupils homework to practice constructing grouped frequency tables, drawing histograms, and estimating the mode.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils reinforce their understanding and are given further practice opportunities.

Lesson Keywords

Grouped Data – Data organized into classes or intervals.
Frequency Table – A table showing how often each item or class appears in a data set.
Class Boundaries – The actual lower and upper limits of a class interval, used to make data continuous.
Histogram – A bar chart for grouped frequency distribution, with adjacent bars.
Mode – The value that appears most frequently in a data set; for grouped data, it is estimated from the histogram.

Differentiation

For struggling learners, the teacher will provide pre-drawn axes and partially completed frequency tables to reduce the workload. Advanced learners will be given more complex data sets or asked to analyze and interpret real-world histograms from newspapers or journals.

Note for teachers using this lesson plan

Ensure that pupils have access to graph papers and drawing instruments. Emphasize the precision required in drawing histograms and estimating the mode. Encourage pupils to practice with various data sets to build their confidence.