Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Identify different data collection methods.
• Construct and interpret frequency tables.
• Create and interpret bar graphs and histograms.
• Construct and interpret pie charts.
• Create and interpret line graphs.

Lesson summary

Data handling is a fundamental skill in Mathematical Literacy, enabling you to make sense of the world around you. In South Africa, we are constantly bombarded with data – from statistics about crime rates and unemployment to information about water usage and electricity consumption. Understanding how to collect, organize, represent, and interpret this data is crucial for informed decision-making, both personally and as active citizens. This week, we will focus on various methods for collecting data and then representing that data in meaningful ways using tables, charts, and graphs.

Lesson notes

2.1 Data Collection Methods Surveys: A survey involves asking a sample of people a set of standardized questions to gather information about their opinions, behaviors, or characteristics. Surveys can be conducted in person, by telephone, by mail, or online.

Example:* A survey asking residents of a township about their access to clean water.

Questionnaires: A questionnaire is a written set of questions designed to collect specific information from individuals. Questionnaires are often used in surveys but can also be used independently.

Example:* A questionnaire distributed to learners at a school to assess their awareness of environmental issues.

Observation: Observation involves systematically watching and recording behavior or events. This method is particularly useful for collecting data in natural settings.

Example:* Observing traffic patterns at a busy intersection to determine peak hours.

Experiments: An experiment is a controlled procedure designed to test a hypothesis. Experiments involve manipulating one or more variables (independent variables) to see how they affect another variable (dependent variable).

Example:* Testing the effectiveness of different fertilizers on crop yields. 2.2 Frequency Tables A frequency table organizes data by showing how many times each value or group of values occurs.

Ungrouped Frequency Tables: Used for discrete data (data that can only take on specific values).

Example:* Number of siblings for each learner in a class.

Grouped Frequency Tables: Used for continuous data (data that can take on any value within a range) or when there are too many different values to make an ungrouped frequency table practical. You need to define class intervals.

Example:* Heights of learners in a class (e.g., 140-149cm, 150-159cm, etc.).

Example 1: Creating a Grouped Frequency Table Suppose we have the following data representing the monthly electricity bills (in Rands) of 20 households in a neighborhood: 350, 420, 580, 610, 480, 520, 390, 450, 550, 680, 720, 410, 590, 650, 500, 470, 630, 700, 560, 440 Steps: Determine the Range: The lowest value is 350 and the highest is

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0. Choose Class Intervals: We'll use intervals of R100: 300-399, 400-499, 500-599, 600-699, 700-

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9. Tally: Count how many values fall into each interval.

Create the Frequency Table: | Electricity Bill (R) | Frequency | |------------------------|-----------| | 300 - 399 | 2 | | 400 - 499 | 6 | | 500 - 599 | 6 | | 600 - 699 | 4 | | 700 - 799 | 2 | 2.3 Bar Graphs and Histograms Bar Graph: Used to represent categorical data (data that can be divided into groups or categories). The height of each bar represents the frequency or relative frequency of that category.

Example:* Favorite sports among Grade 10 learners.

Histogram: Used to represent continuous data (data that can take on any value within a range). The area of each bar represents the frequency or relative frequency of that class interval.

Key Difference: Bars in a histogram touch each other, whereas bars in a bar graph do not (unless consecutive categories exist and should be joined). The x-axis shows the continuous scale.

Example:* Distribution of learners' test scores.

Example 2: Creating a Bar Graph Suppose we asked 30 learners their favorite subject and got the following results: Maths: 10, English: 8, Science: 7, History: 5 Axes: x-axis = Subject, y-axis = Frequency.

Bars: Draw a bar for each subject, with the height corresponding to its frequency.

Labels: Label both axes clearly and give the graph a title (e.g., "Favorite Subjects of Grade 10 Learners").

Example 3: Creating a Histogram Using the electricity bill data from Example 1, create a histogram. The x-axis represents the Electricity Bill (Rands) with each class interval (300-399, 400-499, etc.). The y-axis represents the frequency. Draw the bars adjacent to each other since it's continuous data. 2.4 Pie Charts A pie chart is a circular chart that is divided into sectors, where each sector represents a proportion of the whole. The size of each sector is proportional to the frequency or relative frequency of that category.

Steps: Calculate Sector Angles: For each category, (Frequency / Total Frequency) * 360°.

Draw the Circle: Use a compass to draw a circle.

Draw the Sectors: Use a protractor to draw each sector, starting from 0° and adding the calculated angle for each category.

Label: Label each sector with the category name and/or the percentage it represents.

Example 4: Creating a Pie Chart Suppose we have the following data on household expenditure: Food: 40%, Rent: 30%, Transport: 20%, Other: 10% Sector Angles: Food: (40/100) 360° = 144° Rent: (30/100) 360° = 108° Transport: (20/100) 360° = 72° Other: (10/100) 360° = 36° Draw the Circle and Sectors: Use a compass and protractor.

Label: Label each sector (Food, Rent, Transport, Other) and its percentage. 2.5 Line Graphs A line graph is used to show trends over time.