Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Identify different methods of collecting data.
• Construct and interpret frequency tables.
• Represent data using appropriate graphs like bar graphs, histograms, and pie charts.
• Calculate relative frequencies and percentages.
• Critically evaluate data collection and representation methods.

Lesson summary

Data handling is a crucial skill in today’s world, especially in South Africa where we constantly encounter data related to socio-economic issues, health statistics, and market trends. Being able to collect, organize, represent, and interpret data empowers you to make informed decisions about your life, your community, and your future. For instance, understanding crime statistics can help you make safer choices about where you live or travel. Analysing unemployment rates can inform your career choices. Knowing the spread of diseases like HIV/AIDS or COVID-19 can help you protect yourself and others.

Lesson notes

2.1 Data Collection Methods: Questionnaires: These are a set of written questions used to gather information from a large group of people. Think of surveys about customer satisfaction at a local supermarket or questions about transport preferences for school learners.

Advantages:* Can reach many people relatively cheaply.

Disadvantages:* Low response rates, potential for biased answers (people may answer what they think you want to hear), difficulty in asking clarifying questions.

Surveys: Surveys are similar to questionnaires but can be administered in various ways, including online, by phone, or in person. An example would be a government census to count the population.

Advantages:* Can gather detailed information.

Disadvantages:* Can be time-consuming and expensive.

Observations: This involves watching and recording behaviour or events. For example, observing traffic flow at an intersection to determine the need for traffic lights.

Advantages:* Provides direct information about real-world behavior.

Disadvantages:* Observer bias (the observer's expectations can influence what they see), time-consuming.

Experiments: Experiments involve manipulating one or more variables to see how they affect another variable. For example, testing different fertilizers on maize crops to see which yields the best results.

Advantages:* Can establish cause-and-effect relationships.

Disadvantages:* Can be artificial and not reflect real-world conditions, ethical considerations. 2.2 Frequency Tables: A frequency table is a table that shows how many times each value (or group of values) occurs in a data set.

Example 1: Consider the shoe sizes of 20 learners in your class: 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11,

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2. The frequency table would look like this: | Shoe Size | Frequency | |-----------|-----------| | 6 | 1 | | 7 | 2 | | 8 | 4 | | 9 | 5 | | 10 | 5 | | 11 | 2 | | 12 | 1 | The "frequency" is how many times each shoe size appears.

Grouped Frequency Tables: When dealing with a large range of data, we group the data into intervals. This makes the data easier to understand.

Example 2: Suppose we have the ages of 30 people attending a local clinic: 1, 3, 5, 8, 12, 15, 18, 22, 25, 28, 30, 33, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83,

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6. We can group these ages into intervals of 10: | Age Group | Frequency | |-----------|-----------| | 0-9 | 4 | | 10-19 | 4 | | 20-29 | 4 | | 30-39 | 4 | | 40-49 | 4 | | 50-59 | 4 | | 60-69 | 4 | | 70-79 | 4 | | 80-89 | 2 | 2.3 Graphical Representations: Bar Graphs: Used to compare different categories. The height of each bar represents the frequency or amount for that category. Imagine a bar graph showing the number of learners enrolled in different subjects at your school. Each subject would be a category, and the height of the bar would show the number of learners enrolled.

Histograms: Similar to bar graphs, but used for continuous data that is grouped into intervals. The bars touch each other to show that the data is continuous. Imagine a histogram showing the distribution of heights in a Grade 10 class.

Pie Charts: Used to show the proportion of each category relative to the whole. The entire circle represents 100%, and each slice represents a category. Think about a pie chart showing the different sources of electricity in South Africa.

Line Graphs: Used to show how data changes over time. Points are plotted and connected with lines. For example, a line graph showing the unemployment rate in South Africa over the past 10 years.

Choosing the right graph: Bar Graphs:* For comparing distinct categories.

Histograms:* For showing the distribution of continuous data.

Pie Charts:* For showing proportions.

Line Graphs:* For showing trends over time. 2.4 Relative Frequencies and Percentages: Relative Frequency: The frequency of a category divided by the total frequency.

Percentage: The relative frequency multiplied by

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0. Example 3: Using the shoe size data from Example 1: | Shoe Size | Frequency | Relative Frequency | Percentage | |-----------|-----------|--------------------|------------| | 6 | 1 | 1/20 = 0.05 | 5% | | 7 | 2 | 2/20 = 0.10 | 10% | | 8 | 4 | 4/20 = 0.20 | 20% | | 9 | 5 | 5/20 = 0.25 | 25% | | 10 | 5 | 5/20 = 0.25 | 25% | | 11 | 2 | 2/20 = 0.10 | 10% | | 12 | 1 | 1/20 = 0.05 | 5% | Guided Practice (With Solutions)

Question 1: A local spaza shop owner wants to understand which types of cooldrinks are most popular among his customers. He records the following data for one week: Coke: 30, Fanta: 25, Sprite: 20, Cream Soda: 15, Ginger Ale: 10. (a) Create a frequency table for this data. (b) Represent this data using a bar graph.

Solution: (a)

Frequency Table: | Cooldrink | Frequency | |---------------|-----------| | Coke | 30 | | Fanta | 25 | | Sprite | 20 | | Cream Soda | 15 | | Ginger Ale | 10 | (b)

Bar Graph: (A sketch of the bar graph is expected. Label the x-axis with cooldrink names and the y-axis with frequency.