Class: Junior Secondary School 1 (JSS 1 / JS1)
Term: Third Term
Week: 10
Age: 12 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Data Handling
Previous Lesson: Data Collection, Pictorial Representation of Data, Bar Chart, Line Graph.
Topic: Data Presentation
Subject Matter: Frequency Table and Statistical Averages (Mean, Median, Mode)

Specific Objectives

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

Cognitive Domain:

Define mean, median, and mode.
Construct a frequency table for a given set of data.
Calculate the mean, median, and mode from a given set of data.

Affective Domain:

Appreciate the importance of statistical averages in understanding data.
Show interest in solving problems involving data presentation.

Psychomotor Domain:

Organize raw data efficiently into a frequency table.
Accurately compute the mean, median, and mode for a given data set.

Work collaboratively with peers to solve problems related to data averages.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum
State Unified Scheme of Work
Essential Mathematics for Junior Secondary Schools Book 1
https://www.education.gov.ng
https://www.waecdirect.org

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts showing examples of frequency tables.
Flashcards with definitions of mean, median, and mode.
A whiteboard and markers/chalk.
A prepared data set for practical examples.

Rationale for the Lesson

This lesson helps pupils understand how to organize and interpret numerical data. Knowing how to calculate mean, median, and mode enables pupils to summarize large data sets and make simple comparisons or draw conclusions from everyday information.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic arithmetic operations (addition, division) and can arrange numbers in ascending or descending order.

Lesson Content/Board Summary

Data Presentation: Statistical Averages

Frequency Table

A frequency table is a table that lists items and shows the number of times each item appears in a data set. It helps to organize raw data.

Steps to construct a frequency table:

Draw a table with three columns: ‘Item/Score’, ‘Tally’, and ‘Frequency’.
List each unique item/score in the ‘Item/Score’ column.
Go through the raw data and make a tally mark ( | ) for each occurrence of an item. Group tally marks in fives ( | | | | ) to make counting easier.
Count the tally marks for each item and write the total in the ‘Frequency’ column.

Statistical Averages

Statistical averages are single values that represent a set of data. The most common averages are the mean, median, and mode.

Mean

The mean (or arithmetic mean) is found by adding all the values in a data set and then dividing by the number of values in the set.

Formula: Mean = (Sum of all data values) / (Number of data values)

Example 1: Find the mean of the following scores: 5, 8, 10, 7, 5.

Solution:
Step 1: Sum of scores = 5 + 8 + 10 + 7 + 5 = 35
Step 2: Number of scores = 5
Step 3: Mean = 35 / 5 = 7
The mean score is 7.

Example 2: A pupil scored 65, 70, 80, 75, 60 in five subjects. Calculate the mean score.

Solution:
Step 1: Sum of scores = 65 + 70 + 80 + 75 + 60 = 350
Step 2: Number of subjects = 5
Step 3: Mean = 350 / 5 = 70
The mean score is 70.

Median

The median is the middle value in a data set when the values are arranged in ascending or descending order.

How to find the median:

Arrange the data in ascending (smallest to largest) or descending (largest to smallest) order.
If the number of data values is odd, the median is the middle value.
If the number of data values is even, the median is the average of the two middle values.

Example 1 (Odd number of values): Find the median of: 12, 15, 10, 18, 13.

Solution:
Step 1: Arrange in ascending order: 10, 12, 13, 15, 18
Step 2: Identify the middle value. In this case, it is the 3rd value.
Step 3: The median is 13.

Example 2 (Even number of values): Find the median of: 20, 25, 18, 22, 28, 24.

Solution:
Step 1: Arrange in ascending order: 18, 20, 22, 24, 25, 28
Step 2: Identify the two middle values. These are 22 and 24.
Step 3: Calculate the average of the two middle values: (22 + 24) / 2 = 46 / 2 = 23
The median is 23.

Mode

The mode is the value that appears most frequently in a data set. A data set can have one mode (unimodal), more than one mode (multimodal), or no mode if all values appear with the same frequency.

Example 1: Find the mode of the following data: 3, 5, 7, 5, 9, 3, 5.

Solution:
Step 1: Count the frequency of each number:
3 appears 2 times
5 appears 3 times
7 appears 1 time
9 appears 1 time
Step 2: The number 5 appears most frequently.
Step 3: The mode is 5.

Example 2: Find the mode of the following data: 10, 12, 15, 10, 18, 15.

Solution:
Step 1: Count the frequency of each number:
10 appears 2 times
12 appears 1 time
15 appears 2 times
18 appears 1 time
Step 2: Both 10 and 15 appear most frequently (2 times each).
Step 3: The modes are 10 and 15 (bimodal).

Teaching Methods/Instructional Techniques

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

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and asks them how they can summarize a list of numbers, like scores in a test. The teacher introduces the topic “Data Presentation: Statistical Averages”.
Pupils’ Activity: Pupils respond to the questions and listen attentively.
Learning Point: Pupils are introduced to the concept of summarizing data.

Step 2: Frequency Table

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains what a frequency table is and demonstrates how to construct one using a simple data set on the board, emphasizing the use of tally marks. (e.g., scores: 2,3,4,2,3,5,2,4,3,2).
Pupils’ Activity: Pupils observe the demonstration and ask questions for clarification.
Learning Point: Pupils learn how to organize raw data using a frequency table.

Step 3: Mean

Time: 8 minutes
Teaching Skill: Explanation/Calculation
Teacher’s Activity: The teacher defines the mean and explains its formula. The teacher solves two examples of calculating the mean on the board, involving simple numbers.
Pupils’ Activity: Pupils copy the definition and examples into their notebooks and participate in solving the problems.
Learning Point: Pupils understand how to calculate the mean of a data set.

Step 4: Median

Time: 8 minutes
Teaching Skill: Explanation/Calculation
Teacher’s Activity: The teacher defines the median and explains the steps to find it for both odd and even numbers of data values. The teacher works through two examples on the board.
Pupils’ Activity: Pupils pay attention to the steps, copy examples, and attempt to find the median for practice data.
Learning Point: Pupils learn how to find the middle value (median) in an ordered data set.

Step 5: Mode

Time: 7 minutes
Teaching Skill: Explanation/Identification
Teacher’s Activity: The teacher defines the mode and explains how to identify it by finding the most frequent value. The teacher provides two examples, including one with multiple modes.
Pupils’ Activity: Pupils listen to the explanation, identify modes in given data sets, and copy the examples.
Learning Point: Pupils can identify the most frequent value (mode) in a data set.

Step 6: Combined Example/Practice

Time: 5 minutes
Teaching Skill: Practice/Application
Teacher’s Activity: The teacher gives a new, small data set and asks pupils to work individually or in pairs to find the mean, median, and mode for it.
Pupils’ Activity: Pupils attempt to calculate the three averages for the given data set.
Learning Point: Pupils apply their understanding of mean, median, and mode to a single problem.

Step 7: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

What is a frequency table used for?
Define the term ‘mean’.
How do you find the median of a data set with an even number of values?
Find the mode of the following numbers: 1, 3, 2, 3, 4, 3, 5.

Pupils’ Activity: Pupils answer orally and in writing.
Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the definitions and importance of frequency tables, mean, median, and mode. The teacher assigns homework involving calculating averages from a given data set.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: The lesson is reinforced, and pupils are given practice to consolidate learning.

Home Task: Solve three new exercises on Data Presentation. Show each step and check each answer.

Lesson Keywords

Data – Facts or figures collected for analysis.
Frequency Table – A table showing how often each item occurs in a data set.
Mean – The average of a set of numbers (sum divided by count).
Median – The middle value in an ordered data set.
Mode – The most frequently occurring value in a data set.
Averages – Single values that represent the central tendency of a data set.

Differentiation

For pupils who are struggling, the teacher will provide simpler data sets with fewer numbers and offer one-on-one guidance during practice sessions. For advanced pupils, the teacher will provide more complex data sets, possibly involving larger numbers or asking them to explain real-life scenarios where each average is most appropriate.

Note for teachers using this lesson plan

Ensure pupils understand the importance of arranging data in order before finding the median. Encourage mental arithmetic where possible, but emphasize showing clear working steps for calculations. Provide varied examples to cover different scenarios for mean, median, and mode.