Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Identify sources of bias in South African data.
• Evaluate the appropriateness of different graph types.
• Assess the validity of claims in reports and media.
• Use central tendency and dispersion to evaluate data.
• Analyse the impact of scales and axes on graphs.

Lesson summary

In today's world, we are bombarded with information from various sources – news articles, social media, government reports, and advertisements. Data is presented in numerous formats, including graphs, charts, and summaries.

However, not all data is accurate, reliable, or presented fairly. Being able to critically analyze reports, graphs, and media is an essential life skill. This week's lesson focuses on equipping you with the skills to evaluate the validity and reliability of data representations, identify potential biases, and make informed decisions based on evidence.

Lesson notes

2.1 Sources of Bias: Bias refers to any systematic error or tendency in the data collection, analysis, interpretation, publication, or review of research that can lead to results or conclusions that are systematically different from the truth. Understanding the sources of bias is crucial for critiquing data.

Here are some common sources: Sampling Bias: Occurs when the sample used in a study is not representative of the population. For example, if a survey about cellphone preferences is conducted only among students at a wealthy private school, the results may not reflect the preferences of all South African cellphone users, including those from less affluent backgrounds. Another example would be conducting a survey about the quality of government services only in a predominantly ANC-supporting area.

Response Bias: Occurs when participants provide inaccurate or untruthful answers due to social desirability, recall error, or misunderstanding the question. For instance, when asked about alcohol consumption, people might underestimate their intake due to social stigma. Another example could be related to voting habits – people might falsely claim they voted in an election due to social pressure.

Measurement Bias: Occurs when the method used to measure data is flawed or inaccurate. For instance, using a faulty thermometer to measure temperature or an outdated survey instrument can lead to measurement bias. This can also include using questions that are leading or confusing.

Publication Bias: Occurs when studies with positive or significant results are more likely to be published than studies with negative or non-significant results. This can lead to an overestimation of the effect of a particular intervention or phenomenon.

Funding Bias: Occurs when the source of funding for research influences the results or interpretation of the data. For example, research funded by a tobacco company may be less likely to find harmful effects of smoking. 2.2 Appropriateness of Graph Types: Choosing the right graph type is crucial for effectively communicating data. Using an inappropriate graph can distort the information and lead to misinterpretations.

Pie Charts: Best used to show parts of a whole. Each slice represents a percentage of the total. They are not suitable for comparing multiple data sets or showing trends over time.

Example: Showing the percentage distribution of different ethnic groups in a South African province. Be aware that when the percentages are very close, the pie chart can be misleading.

Bar Graphs: Useful for comparing different categories of data. Bar graphs can be vertical (column graphs) or horizontal.

Example: Comparing the number of crimes reported in different provinces of South Africa.

Line Graphs: Ideal for showing trends over time.

Example: Tracking the unemployment rate in South Africa over the past 10 years. It is important to consider the scale of the axes; manipulation of the scale can exaggerate or diminish a trend.

Histograms: Used to display the distribution of continuous data. The data is grouped into intervals (bins), and the height of each bar represents the frequency of values within that interval.

Example: Showing the distribution of household income levels in a community.

Scatter Plots: Used to show the relationship between two variables. Each point represents a data point with values for both variables.

Example: Investigating the correlation between education level and income. 2.3 Measures of Central Tendency and Dispersion: These measures provide summary statistics about a dataset.

Mean: The average of all values in a dataset. Calculated by summing all the values and dividing by the number of values.

Example: Calculating the average monthly expenditure of a household.

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

Example: Determining the median salary of employees in a company.

Mode: The value that appears most frequently in a dataset.

Example: Identifying the most popular brand of maize meal in a community.

Range: The difference between the highest and lowest values in a dataset.

Example: Determining the range of temperatures recorded in a city over a month.

Standard Deviation: A measure of how spread out the data is from the mean. A higher standard deviation indicates greater variability. This is a more reliable measure of spread than range, particularly with outliers. The formula for sample standard deviation is s = sqrt[ Σ(xi – x̄)^2 / (n – 1)] where xi is each data point, x̄ is the mean, and n is the number of data points. Calculating this is not always practical without technology.