Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Identify common ways data is misrepresented in graphs.
• Critique the choice of graph for a specific dataset.
• Analyse media reports for bias in data or presentation.
• Understand how mean, median, and mode can be used or misused.
• Evaluate the reliability and validity of a data source.

Lesson summary

Data handling is a crucial skill in today's information-saturated world. We are constantly bombarded with data presented in reports, graphs, and media articles. Being able to critically analyze this information is vital to making informed decisions, whether it's about choosing a cellphone contract, understanding crime statistics in your neighbourhood, or interpreting the government's budget allocation for education. In South Africa, with our diverse socio-economic landscape, understanding how data can be manipulated or misrepresented is particularly important for civic engagement and social justice.

Lesson notes

2. 1. Introduction to Critiquing Data Critiquing data involves questioning the data's source, how it was collected, how it is presented, and what conclusions are drawn from it. It's about being a skeptical consumer of information rather than accepting it at face value. 2.

2. Common Techniques for Misrepresenting Data: Truncated Axes: Starting the y-axis of a graph at a value other than zero can exaggerate the difference between data points, making a small change appear significant.

Example: A graph showing the decrease in crime rates in a city might start the y-axis at 100 incidents instead of

0. This makes the decrease look much larger than it actually is.

Misleading Scaling: Using inconsistent or inappropriate scales on the axes can distort the visual representation of the data.

Example: A graph comparing the price of bread over time might use different intervals on the x-axis (time), making periods with small price increases appear longer and therefore more significant.

Selective Data Presentation: Only presenting data that supports a particular viewpoint while omitting contradictory evidence.

Example: A political party might release crime statistics showing a decrease in overall crime but fail to mention that specific types of crime (e.g., house robberies) have increased significantly.

Cherry-Picking Data: Selecting specific time periods or data points to support a particular claim.

Example: Highlighting only the months where a company's sales were high to create a positive impression, ignoring months with poor sales. Correlation vs.

Causation: Mistaking a correlation (a relationship between two variables) for causation (one variable causing the other).

Example: An article might claim that increased cellphone use causes lower matric results, simply because both have increased over time. This ignores other potential factors, such as changes in the curriculum or socio-economic conditions.

Inappropriate Graph Types: Choosing a graph type that is unsuitable for the data being presented.

Example: Using a pie chart to compare the growth of different sectors of the economy over time. A bar chart or line graph would be more appropriate for showing trends over time.

Sample Size Issues: Drawing conclusions from a sample size that is too small to be representative of the population.

Example: Conducting a survey of only 20 students at a single school and using the results to make generalizations about all students in South Africa. 2.

3. Descriptive Statistics: Mean, Median, and Mode These measures provide a summary of the central tendency of a dataset.

However, they can also be manipulated or misinterpreted.

Mean (Average): The sum of all values divided by the number of values.

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

Example: Salaries of employees in a small company: R10 000, R12 000, R15 000, R20 000, R100 000 (CEO). The mean salary is (10000 + 12000 + 15000 + 20000 + 100000) / 5 = R31

4

0

0. The mean is highly influenced by the outlier (CEO's salary).

Median (Middle Value): The middle value when the data is arranged in ascending order. If there's an even number of values, the median is the average of the two middle values.

Example: Using the same salary data: R10 000, R12 000, R15 000, R20 000, R100

0

0

0. The median salary is R15

0

0

0. The median is less affected by outliers.

Mode (Most Frequent Value): The value that appears most often in the dataset.

Example: Number of children per household in a neighbourhood: 0, 1, 1, 2, 2, 2, 3,

4. The mode is 2 (2 children per household is the most common). 2.

4. Reliability and Validity of Data Sources Reliability: The consistency and repeatability of the data. A reliable source will produce similar results if the data collection process is repeated.

Validity: The accuracy and truthfulness of the data. A valid source measures what it is intended to measure.

Factors to consider: Source Credibility: Is the source reputable and unbiased?

Data Collection Methods: Were the data collection methods sound and free from bias?

Sample Selection: Was the sample representative of the population?

Transparency: Does the source provide clear information about its methodology and data sources? Guided Practice (With Solutions)

Question 1: A graph shows the number of tourists visiting Durban over the past 5 years. The y-axis starts at 500,000 tourists.

The values are: Year 1: 520,000; Year 2: 530,000; Year 3: 545,000; Year 4: 560,000; Year 5: 575,000. a) Explain how the truncated y-axis can be misleading. b) Redraw the graph with the y-axis starting at

0. How does this change the visual representation?

Solution: a) The truncated y-axis exaggerates the increase in tourist numbers. It makes the growth appear much more significant than it actually is. Someone looking at the graph might think tourism has increased dramatically, when in reality, the increase is relatively small compared to the overall number of tourists. b) [Students should redraw the graph.