Basic Statistical Measures and their Graphical Representations for SS 1

Class: SS 1
Term: Second Term
Week: 7
Age: 15 years
Duration: 60 minutes
Subject: Digital Technologies
Curriculum Theme: Data Science
Focal competence: Using appropriate software tools to graphically represent data and make interpretations
Key competencies/values: Communication
Skills:

• Generating meaningful charts and graphs from raw data
• Identifying trends and patterns

Previous Lesson: Structured and Unstructured Data, Examples, Characteristics and Importance
Topic: Basic Statistical Measures And Their Graphical Representations
Subject Matter: Meaning of Basic Statistical Measures and their Graphical Representations, Basic Statistical Concepts

Specific Objectives

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

Cognitive Domain

• Define Basic Statistical Measures and their Graphical Representations.
• Interpret basic statistical values.
• Describe the basic statistical concepts with examples.

Affective Domain

• Appreciate the importance of data representation in various fields.
• Participate actively in discussions about statistical concepts.

Psychomotor Domain

• Use simple data collection methods to gather data of events within their environment.
• Use software tools to create appropriate graphical representation of data.

Reference Materials

The following resources were used in planning this lesson:

• 2025 New Revised Senior Secondary Education Curriculum (SSEC)
• Relevant State Unified Scheme of Work
• A suitable Digital Technologies textbook for SS 1
• The HeadTeacher Scheme of work For The New Revised Senior Secondary Education Curriculum (SSEC)

Instructional Materials

The teacher will teach this lesson with the aid of:

• Computers/laptops with internet access
• Spreadsheet software (e.g., MS Excel, Google Sheets)
• Projector and screen (optional, for demonstration)
• Sample data sets from everyday events (e.g., students’ test scores, daily temperatures)

Rationale for the Lesson

This lesson is important as it equips students with fundamental skills in understanding and presenting data, which is crucial in today’s data-driven world. It helps them make sense of information, identify trends, and communicate findings effectively using digital tools. Mastering these concepts supports informed decision-making and problem-solving in various academic and real-life scenarios.

Prerequisite/Previous Knowledge

Students should have basic computer literacy, including familiarity with operating a computer and opening applications. They should also have a foundational understanding of numbers and simple arithmetic operations.

Lesson Content/Board Summary

Basic Statistical Measures And Their Graphical Representations

Meaning of Basic Statistical Measures

Basic Statistical Measures are numerical values that summarise and describe the main features of a dataset. These measures help to understand the central tendency, spread, and distribution of data, making it easier to interpret large amounts of information.

Meaning of Graphical Representations

Graphical representations are visual displays of data using charts, graphs, and diagrams. They help to present statistical information in an easy-to-understand format, making patterns, trends, and comparisons more evident than raw numbers alone. Common types include bar charts, pie charts, and line graphs.

Basic Statistical Concepts

Mean

The Mean (also known as the average) is calculated by summing all the values in a dataset and dividing the sum by the total number of values. It represents the central value of a dataset.

Formula:

( text{Mean} = frac{sum x}{n} )

Where:

1. ( sum x ) = Sum of all values
2. ( n ) = Total number of values

Example 1

Question: Calculate the mean of the following scores: 2, 3, 5, 5, 7, 8, 10.

Solution:

Step 1: Sum all the values.

( sum x = 2 + 3 + 5 + 5 + 7 + 8 + 10 = 40 )

Step 2: Count the total number of values.

( n = 7 )

Step 3: Divide the sum by the number of values.

( text{Mean} = frac{40}{7} approx 5.71 )

Answer: The mean is approximately 5.71.

Median

The Median is the middle value in a dataset when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.

Example 1

Question: Find the median of the scores: 2, 3, 5, 5, 7, 8, 10.

Solution:

Step 1: Arrange the scores in ascending order (they are already arranged).

2, 3, 5, 5, 7, 8, 10

Step 2: Identify the middle value. There are 7 values, so the middle value is the 4th value.

Answer: The median is 5.

Example 2

Question: Find the median of the scores: 2, 3, 5, 7, 8, 10.

Solution:

Step 1: Arrange the scores in ascending order (they are already arranged).

2, 3, 5, 7, 8, 10

Step 2: Identify the two middle values. There are 6 values, so the middle values are the 3rd and 4th values.

Middle values are 5 and 7.

Step 3: Calculate the average of the two middle values.

( text{Median} = frac{5 + 7}{2} = frac{12}{2} = 6 )

Answer: The median is 6.

Mode

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

Example 1

Question: Find the mode of the scores: 2, 3, 5, 5, 7, 8, 10.

Solution:

Step 1: Observe which value appears most often.

The value ‘5’ appears twice, which is more than any other value.

Answer: The mode is 5.

Example 2

Question: Find the mode of the scores: 2, 3, 5, 7, 8, 10.

Solution:

Step 1: Observe which value appears most often.

All values appear only once.

Answer: There is no mode for this dataset.

Range

The Range is the difference between the highest (maximum) value and the lowest (minimum) value in a dataset. It gives a simple measure of the spread or variability of the data.

Formula:

( text{Range} = text{Highest Value} – text{Lowest Value} )

Example 1

Question: Calculate the range of the scores: 2, 3, 5, 5, 7, 8, 10.

Solution:

Step 1: Identify the highest value.

Highest Value = 10

Step 2: Identify the lowest value.

Lowest Value = 2

Step 3: Subtract the lowest value from the highest value.

( text{Range} = 10 – 2 = 8 )

Answer: The range is 8.

Percentages

A Percentage is a way of expressing a number as a fraction of 100. It is often used to show proportions or parts of a whole.

Formula:

( text{Percentage} = left( frac{text{Part}}{text{Whole}} right) times 100% )

Example 1

Question: In a class of 40 students, 10 students passed a test. What percentage of students passed the test?

Solution:

Step 1: Identify the part and the whole.

Part (students who passed) = 10

Whole (total students) = 40

Step 2: Apply the percentage formula.

( text{Percentage} = left( frac{10}{40} right) times 100% )

Step 3: Calculate the percentage.

( text{Percentage} = 0.25 times 100% = 25% )

Answer: 25% of the students passed the test.

Teaching Methods/Instructional Techniques

Discussion, Explanation, Demonstration, Guided Practice, Question and Answer, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Questioning/Discussion

Teacher’s Activity: The teacher greets the students and asks them how numbers are used in everyday life, for example, in sports scores, election results, or school grades. The teacher then introduces the topic of basic statistical measures and their importance in understanding data.

Pupils’ Activity: Pupils respond to the questions and share examples of how numbers are used around them.

Learning Point: Real-life data applications

Step 2: Meaning of Basic Statistical Measures

Time: 10 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher explains what basic statistical measures are, emphasising their role in summarising data. The teacher also introduces the concept of graphical representations as visual tools for data. The teacher guides students to discuss the basic statistical concepts and the application of statistics in real life.

Pupils’ Activity: Pupils listen, ask questions, and contribute to the discussion on the application of statistics.

Learning Point: Definition of statistics

Step 3: Basic Statistical Concepts – Mean, Median, Mode

Time: 15 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher defines Mean, Median, and Mode, providing clear examples for each using a simple dataset. The teacher demonstrates how to calculate each measure step-by-step on the board or using a projector.

Pupils’ Activity: Pupils listen, copy definitions, and follow along with the examples, attempting calculations.

Learning Point: Central tendency measures

Step 4: Basic Statistical Concepts – Range and Percentages

Time: 10 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher defines Range and Percentages, explaining their importance in understanding data spread and proportions. The teacher provides examples and demonstrates calculations for both concepts.

Pupils’ Activity: Pupils listen, copy definitions, and work through examples with the teacher.

Learning Point: Data spread and proportion

Step 5: Graphical Representations and Software Tools

Time: 10 minutes

Teaching Skill: Demonstration/Guided Practice

Teacher’s Activity: The teacher demonstrates how to use spreadsheet software (e.g., MS Excel or Google Sheets) to calculate Mean, Median, Mode, and Range. The teacher then shows how to create simple graphical representations (e.g., bar chart, pie chart) from a given dataset using the software. The teacher guides students to use simple data collection methods to gather data of events within their environment.

Pupils’ Activity: Pupils observe the demonstration, ask questions, and if resources permit, attempt to follow along on their own computers or in pairs.

Learning Point: Data visualisation with software

Step 6: Practical Application and Interpretation

Time: 5 minutes

Teaching Skill: Application/Interpretation

Teacher’s Activity: The teacher provides a simple dataset (e.g., daily attendance for a week) and asks students to identify the mean, median, mode, and range, and suggest an appropriate graphical representation. The teacher guides them to interpret what the calculated values and chosen graph tell them about the data.

Pupils’ Activity: Pupils work individually or in pairs to analyse the data and interpret the results.

Learning Point: Interpreting statistical values

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

1. Define Basic Statistical Measures.
2. What is the difference between Mean and Median?
3. Given the data set: 12, 15, 10, 15, 18. Calculate the Mode and Range.
4. Mention two types of graphical representations.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Understanding statistical concepts

Step 8: Note-Taking

Time: 10 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes, including definitions, formulas, and examples of statistical measures and graphical representations, into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Recording lesson content

Step 9: Conclusion

Time: 5 minutes

Teaching Skill: Summarising

Teacher’s Activity: The teacher briefly recaps the importance of basic statistical measures and graphical representations in understanding and communicating data. The teacher encourages students to practice using spreadsheet software for data analysis.

Pupils’ Activity: Pupils listen and ask any final questions.

Learning Point: Recap of key concepts

Continuous Assessment/Further Study

Type: Homework

Instruction: Answer the following questions in your Digital Technologies notebook.

1. Collect the scores of 10 students in their last Digital Technologies test.
2. Calculate the Mean, Median, Mode, and Range of these scores.
3. Using a spreadsheet software (e.g., MS Excel or Google Sheets), create a bar chart to represent these scores.
4. What percentage of students scored above the mean?

Lesson Keywords

• Mean – The average of a set of numbers.
• Median – The middle value in an ordered dataset.
• Mode – The most frequently occurring value in a dataset.
• Range – The difference between the highest and lowest values in a dataset.
• Percentage – A fraction of 100, used to express proportions.
• Data – Facts and statistics collected together for reference or analysis.
• Statistics – The practice or science of collecting and analysing numerical data.
• Graphical Representation – Visual display of data using charts or graphs.
• Spreadsheet Software – Application used to organise, analyse, and store data in tabular form (e.g., MS Excel).

Differentiation

Support: Provide simpler datasets for calculations and offer step-by-step guides for using spreadsheet software. Pair struggling students with more proficient ones for guided practice.

Extension: Challenge advanced students to explore other statistical measures (e.g., standard deviation) or create more complex charts (e.g., scatter plots) using larger datasets. Encourage them to research real-world applications of statistics in different fields.

Suggested Lesson Videos

For further understanding, search on YouTube for:

• “Basic Statistical Measures for SS1 Digital Technologies”
• “How to create charts in MS Excel for beginners”
• “Mean Median Mode Range explained with examples”