Mathematics - Senior Secondary 2 - Grouped Data (Drawing and Reading of Histogram)

Grouped Data (Drawing and Reading of Histogram)

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TERM: 3RD TERM

Week: 2

Class: Senior Secondary School 2
Age: 16 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Grouped Data (Drawing and Reading of Histogram)
Focus: Grouping data, constructing grouped frequency tables, calculating class boundaries, class intervals, and class marks.

 

SPECIFIC OBJECTIVES:

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

  1. Appreciate the need for grouping data.
  2. Construct a grouped frequency table from raw data.
  3. Calculate class boundaries, class intervals, and class marks.
  4. Draw and read histograms from grouped data.

 

INSTRUCTIONAL TECHNIQUES:

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

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Poles of different heights
  • Objects representing different categories (e.g., ages, prices, objects with varying sizes, etc.)
  • Flashcards with sample data
  • Graph paper for drawing histograms
  • Calculator for calculations

 

PERIOD 1 & 2: Introduction to Grouped Data and Frequency Tables

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Teacher asks students to suggest and write down possible scores of 50 students in mathematics.

Students suggest scores and record them.

Step 2 - Need for Grouping

Teacher explains why raw data must often be grouped (for clarity and simplicity). Demonstrates grouping scores into ranges (e.g., 40-49, 50-59).

Students discuss the need for grouping and observe the teacher’s demonstration.

Step 3 - Grouped Frequency Table

Teacher constructs a grouped frequency table from the suggested scores, using appropriate intervals.

Students observe the construction and record the table in their notebooks.

Step 4 - Class Boundaries, Intervals, and Marks

Teacher explains how to calculate class boundaries, class intervals, and class marks using the grouped data.

Students calculate class boundaries, intervals, and class marks based on the example.

NOTE ON BOARD:

  • Grouped frequency table format:

Class Interval

Frequency

Class Boundaries

Class Mark

40-49

10

39.5-49.5

44.5

50-59

15

49.5-59.5

54.5

 

EVALUATION (5 Exercises):

  1. What is the purpose of grouping data?
  2. How do you calculate class marks?
  3. How do you find the class boundaries?
  4. What is a class interval in a grouped frequency table?
  5. In what situations might you use grouped data?

 

CLASSWORK (5 Questions):

  1. Given the data: 12, 14, 18, 22, 25, 28, 31, 34, 36, 38, construct a grouped frequency table with a class interval of 5.
  2. Calculate the class boundaries and class marks for the above data.
  3. In a frequency table, how would you calculate the frequency for a given class interval?
  4. What is the class mark for the interval 10-19?
  5. Draw a grouped frequency table for the following data: 35, 42, 43, 50, 56, 59, 62, 65, 68, 75.

 

ASSIGNMENT (5 Tasks):

  1. Construct a grouped frequency table for the following ages of 50 students: 14, 17, 20, 23, 19, 21, 16, 22, 18, 25.
  2. Calculate the class boundaries and class marks for the above table.
  3. What is the importance of grouping data in statistical analysis?
  4. Define a frequency polygon and explain how it relates to histograms.
  5. Research real-life examples where grouped data is used (e.g., market prices, heights of people).

 

PERIOD 3 & 4: Drawing and Reading Histograms

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Histograms

Teacher introduces histograms and explains their role in visualizing grouped data. Shows an example histogram.

Students observe and discuss the example histogram.

Step 2 - Drawing a Histogram

Teacher demonstrates how to draw a histogram from a grouped frequency table.

Students follow the demonstration and begin drawing their histograms.

Step 3 - Reading a Histogram

Teacher explains how to read and interpret a histogram, focusing on identifying the frequency of each class interval.

Students practice reading histograms and identifying frequency distributions.

NOTE ON BOARD:

  • A histogram is a bar graph where:
    • The x-axis represents the class intervals.
    • The y-axis represents the frequencies.
    • Each bar’s height represents the frequency of a class interval.

 

EVALUATION (5 Exercises):

  1. Draw a histogram for the following data:

Class Interval

Frequency

0-9

5

10-19

8

20-29

3

30-39

4
  1. From the histogram you drew, what is the frequency of the 10-19 interval?
  2. How do you know if a histogram is accurately drawn?
  3. What does the height of a bar in a histogram represent?
  4. What is the x-axis label on a histogram?

 

CLASSWORK (5 Questions):

  1. Draw a histogram for the following data:

Class Interval

Frequency

0-5

7

6-10

10

11-15

5

16-20

3
  1. What is the class interval with the highest frequency in the histogram?
  2. How can you tell which class interval has the lowest frequency?
  3. What is the class mark for the interval 6-10?
  4. How does the width of the bars in a histogram relate to the class intervals?

 

ASSIGNMENT (5 Tasks):

  1. Draw a histogram for the following grouped data:

Class Interval

Frequency

10-20

6

21-30

4

31-40

8

41-50

3
  1. Calculate the class marks and boundaries for the above data.
  2. What is the difference between a histogram and a bar chart?
  3. Find the frequency for the interval 21-30 from the given histogram.
  4. Write a short paragraph explaining the benefits of using histograms in data analysis.