Media Bias & Statistical Analysis
Misleading vs Fair Graph Techniques
Sort each data presentation technique into the correct column: Misleading or Fair.
Misleading Technique → Why It's Problematic
Draw a line from each misleading technique to the reason it distorts data.
Spot the Problem — Graphs
Circle the main problem with each graph description.
A bar chart comparing company profits starts its y-axis at $9.5 million instead of $0.
A pie chart has five slices that add up to 120%.
A line graph of 'yearly rainfall' uses data from only January to March.
A pictograph uses one icon = 10 units in the first row but one icon = 50 units in the second row.
Sample Size & Representativeness
Circle the BEST critique of each survey's sampling method.
A toothpaste brand surveys 5 dentists and claims '4 out of 5 dentists recommend our product.'
A political poll interviews 2 000 people, all from one suburb in Sydney.
An online survey asks visitors to a fitness website whether they exercise daily.
A school surveys every student in Years 7–12 about canteen food preferences.
Biased vs Unbiased Sampling Methods
Sort each sampling method into the correct column: Biased or Unbiased.
Mean, Median, or Mode — Which Is Best?
Circle the BEST measure of centre for each data set.
House prices in a suburb: $450k, $470k, $480k, $490k, $3.2 million
Shoe sizes sold in a shop last week: 8, 9, 9, 9, 10, 10, 11
Test scores evenly spread from 55 to 95 with no outliers
Annual salaries at a startup: $60k, $62k, $65k, $65k, $900k (CEO)
Measure of Centre → When to Use It
Draw a line from each measure of centre to the scenario where it is most appropriate.
Who Was Asked? — Identify the Audience
Circle the statement that correctly identifies a problem with who was surveyed.
A car magazine survey finds that 90% of people think cars are better than public transport.
A soft-drink company surveys teenagers at a music festival about their favourite drinks.
A government health survey randomly selects 5 000 households across all states and territories.
Valid Conclusions from Survey Data
Circle the VALID conclusion that can be drawn from each scenario.
A survey of 50 students at a private school found that 80% prefer organic food. Headline: 'Most Australians prefer organic food.'
A nationwide random survey of 10 000 adults finds that 62% support renewable energy. Margin of error: ±2%.
A company surveys its own employees and finds 95% are satisfied. Headline: 'Workers love their jobs.'
Identify Confounding Variables
Circle the most likely confounding variable in each scenario.
A study finds that children who eat breakfast score higher on maths tests.
Towns with more police officers have higher crime rates.
People who own more books tend to live longer.
Countries that consume more chocolate win more Nobel Prizes.
Correlation vs Causation in Media Claims
Circle the correct interpretation of each media claim.
A graph shows ice cream sales and drowning rates both increase in summer.
'Countries that spend more on education have higher GDP.'
'People who sleep with their shoes on are more likely to wake up with a headache.'
Misleading Percentages
Circle the correct response to each percentage claim.
An ad claims: 'Our cereal has 50% less sugar!' But it was reduced from 2 g per serve to 1 g per serve.
A headline states: 'Disease X cases doubled!' Cases went from 2 to 4 in a city of 1 million.
A politician says unemployment dropped from 5.0% to 4.8% and calls it 'a massive improvement.'
A supplement company claims their product 'triples your chance of recovery' — from 1% to 3%.
Steps to Evaluate a Statistical Claim
Put the steps for critically evaluating a statistical claim into the correct order.
Logical Fallacy → Example
Draw a line from each logical fallacy to its correct example.
Headline vs Reality
Circle the response that best describes the gap between the headline and the actual data.
Headline: 'Teen Screen Time SKYROCKETS!' Data: Average daily screen time for teens rose from 6.8 hours to 7.1 hours over 2 years.
Headline: 'MAJORITY of residents oppose the new park.' Survey: 52% opposed, 48% supported, margin of error ±4%.
Headline: 'Miracle Fruit Cuts Cancer Risk by 50%!' Study: Participants who ate the fruit daily for 10 years had a 0.02% cancer rate vs 0.04% in the control group.
Questions to Ask About a Statistic
Sort each item into the correct column: Important Question to Ask or Not Particularly Relevant.
Effect of Outliers on Mean vs Median
Circle the correct statement about how outliers affect each measure.
Data set: 12, 14, 15, 16, 17, 98. What happens to the mean vs the median?
A company reports the 'average salary' is $120 000. Which is most likely true?
If you remove the single highest value from a data set, which measure changes more?
Absolute vs Relative Change
Circle the response that correctly interprets each claim using absolute and relative change.
A charity says donations rose 200% — from $50 to $150.
A headline says 'Shark attacks up 50%!' Last year: 2 attacks. This year: 3 attacks.
A drug reduces heart attack risk by 25%. The control group had a 4% risk; the drug group had a 3% risk.
Critique a Truncated Y-Axis Bar Chart
Analyse the following scenario and write a detailed critique.
A news headline states: 'Crime has DOUBLED!' The bar chart shows crime incidents going from 498 to 512, but the y-axis starts at 490. Explain: (a) why the truncated y-axis makes the increase look much larger than it is, (b) what the actual percentage increase is, (c) how the graph should be presented fairly, and (d) why a reader who only glances at the chart might be misled.
Evaluate a Media Claim About Violent Crime
Critically evaluate the following media claim.
A social media post claims: 'Australia is getting more dangerous — violent crime rose 8% last year!' List at least 5 questions you would ask before accepting or rejecting this claim. Consider: sample and data source, definition of 'violent crime', population growth, historical trends, and whether reporting rates have changed.
Analyse a Misleading Advertisement Statistic
Write a critical analysis of the following advertisement.
A weight-loss supplement ad claims: '95% of users lost weight in just 4 weeks!' In small print, the study had 20 participants, was funded by the supplement company, had no control group, and 'weight loss' was defined as losing at least 100 grams. Write a critical analysis covering: (a) why the sample size is a problem, (b) why the funding source matters, (c) why a control group is needed, and (d) why the definition of 'weight loss' is misleading.
Compare Two News Sources Reporting the Same Data
Analyse how the same data can be framed differently.
Two news outlets report on the same employment data. Source A headline: 'Economy booming — 50 000 new jobs created!' Source B headline: 'Job crisis deepens — unemployment still above 5%.' Both are citing the same government report. Explain: (a) how each source selected different aspects of the data to support its narrative, (b) what additional context a reader would need, (c) which framing (if either) is more honest, and (d) how you would write a balanced headline.
Design a Fair Survey
Apply your knowledge of sampling and bias to design an unbiased survey.
You want to find out whether students in your state support later school start times. Design a fair survey by describing: (a) your target population and sample size, (b) your sampling method and why it reduces bias, (c) at least 3 unbiased survey questions (avoid leading questions), (d) how you would report the results honestly, including margin of error and limitations.
True or False — Statistical Literacy
Circle TRUE or FALSE for each statement.
A correlation of 0.95 between two variables proves that one causes the other.
If a graph's y-axis starts at a value other than 0, it is always misleading.
A larger sample size generally gives more reliable results.
The median is always a better measure of centre than the mean.
If a study is funded by a company with a financial interest in the results, the findings should be treated with extra scrutiny.
Rewrite a Misleading Headline
Rewrite each misleading headline to be accurate and fair.
Misleading headline: 'DEADLY new disease sweeps the nation — cases up 300%!' Reality: Cases rose from 3 to 12 nationwide (population 26 million), the disease is rarely fatal, and the increase is partly due to improved testing. Rewrite the headline to be accurate, then explain in 2–3 sentences why the original was misleading.
Misleading headline: 'Students today are the worst readers in history!' Reality: Average reading scores dropped by 2 points on a 500-point scale compared to 10 years ago, while participation in the assessment increased by 15% (including more students with learning difficulties). Rewrite the headline to be accurate, then explain why the original was misleading.
Why 'Average' Can Be Misleading
Explain how the word 'average' can be used to mislead.
A real estate agent says: 'The average home in this suburb sold for $1.2 million last year.' There were 10 sales: nine homes sold for between $600k and $750k, and one waterfront mansion sold for $6 million. (a) Calculate the approximate mean and median sale prices. (b) Explain why the agent chose to report the mean. (c) Which measure would be more useful for a buyer looking at typical homes in the suburb? (d) How could the agent present the data honestly?
Media Literacy Challenge
Critically examine statistics used in the media.
- 1Find a graph or statistic in a news article, advertisement, or social media post. Identify at least 3 potential sources of bias or misleading presentation (e.g. truncated axis, small sample, missing context). Write down how you would improve the presentation.
- 2Watch a news segment that uses statistics. Record: the claim, the evidence given, and any missing information (sample size, methodology, who funded the research, margin of error). Rate the claim's reliability out of 10 and justify your rating.
- 3Compare how two different news sources report on the same statistic (e.g. employment, housing prices, crime rates). Note the differences in framing, headline language, and which data each source chose to highlight or omit.
Create Your Own Fair Infographic
Apply what you have learned to create an honest, well-designed infographic.
- 1Choose a topic you care about (sport, environment, music, gaming, etc.) and find real data from a reliable source (ABS, government report, reputable news outlet).
- 2Create a hand-drawn or digital infographic that presents the data fairly: use a y-axis starting at 0 (or clearly label it if not), include sample sizes and sources, use consistent scales, and avoid cherry-picking.
- 3Write a short paragraph underneath your infographic explaining the design choices you made and why they help the reader understand the data honestly.
Misleading Statistics — Identify and Critique
Identify and explain how statistics can be misleading.
A shampoo advertisement claims: 'In a study of 50 people, 90% noticed reduced hair fall.' Identify at least 3 reasons this statistic might be misleading or unreliable.
A newspaper reports: 'Hospital admissions rose by 50% during the long weekend.' The actual numbers were 6 admissions on a normal day and 9 on the long weekend. Explain why this is technically correct but potentially misleading.
Statistical Bias Types
Draw a line from each bias type to its correct description.
Identify the Misleading Graph Technique
Circle the technique used to mislead in each graph description.
A bar chart where the y-axis starts at 95 instead of 0, making a small difference look huge:
A line graph that shows data for only the past 3 months of a 10-year period where the trend favours the claim:
A 3D pie chart where the front slice appears much larger than its true proportion:
Comparing two bar charts with different y-axis scales placed side by side:
Mean, Median, Mode — Which to Use?
Choose and justify the appropriate measure of centre for each context.
Household incomes in a suburb: $45,000; $52,000; $48,000; $51,000; $1,200,000. Calculate the mean, median, and mode. Which best represents a 'typical' household income? Why does the millionaire distort the mean?
A shoe shop records sizes sold in one day: 8, 9, 9, 9, 10, 10, 11, 12, 13. Which measure of centre is most useful for the shop manager deciding which sizes to reorder? Why?
Sample vs Population
Sort each situation: describes a Sample or a Population.
Sampling Methods — Compare and Evaluate
Compare different sampling methods and their limitations.
A researcher wants to estimate the average screen time of Year 10 students in Australia. Compare three sampling methods: (a) simple random sample, (b) stratified sample (by state), (c) convenience sample (asking students at the local library). For each, describe how the sample would be selected and identify a potential source of bias.
Standard Deviation — Interpretation
Circle the correct interpretation of standard deviation for each scenario.
Test scores: Mean = 70, SD = 3. This means:
Two classes: Class A has SD = 2, Class B has SD = 12 (both have mean 65). Which is more consistent?
On a normal distribution, approximately 68% of data falls within:
Box Plots — Construct and Compare
Construct box plots and use them for comparison.
For the data set: 12, 15, 18, 21, 22, 23, 25, 28, 30, 35, 42 (a) Find the median, Q1, Q3, minimum, and maximum. (b) Calculate the IQR. (c) Identify any outliers using: value < Q1 − 1.5×IQR or value > Q3 + 1.5×IQR. (d) Describe the shape of the distribution.
Graph Type to Best Use
Draw a line from each graph type to its best statistical use.
Statistical Reports — Evaluate and Rewrite
Critically read and improve a flawed statistical report.
A health department report states: '75% of people who ate our new supplement felt healthier.' The study involved 20 volunteers who self-reported their health. Identify at least 4 flaws in this study (sample size, self-report, no control group, etc.). Suggest how each flaw could be corrected for a more valid study.
Media Statistical Analysis
Critically analyse statistics used in Australian media.
- 1Find a news article that uses a statistic to support a claim (e.g. about health, crime, economy). Identify: the statistic used, the source, the sample size if given, and any potential bias or missing context. Write a one-paragraph critical evaluation.
- 2Watch a political advertisement or read a political press release. Identify every statistical claim made. Look up the original source (if provided) and check whether the statistics are being used accurately and in context.
- 3Compare how two different Australian newspapers report the same statistic or survey result. Do they emphasise different aspects? Do they use different chart types or scales?
Skewness and Data Distribution
Describe and interpret skewed distributions.
Explain the difference between a positively skewed and negatively skewed distribution. For each type, state: (a) the shape of the histogram, (b) which measure (mean or median) is larger, (c) give a real-world example of data with that skew.
House prices in a suburb have mean $850,000 and median $720,000. (a) Is the distribution positively or negatively skewed? (b) Which measure better represents the 'typical' house price? (c) What kind of data point would cause this skew?
Classify: Good Sampling Practice vs Poor Sampling Practice
Sort each practice into Good or Poor sampling practice.
Types of Statistical Errors Found in Media
Tally each type of statistical error you find while reviewing 20 news articles or reports.
| Item | Tally | Total |
|---|---|---|
Misleading graph (truncated axis, 3D) | ||
Small or biased sample | ||
Confusing correlation with causation | ||
Missing context or baseline | ||
Cherry-picked data range |
Interquartile Range and Outliers
Use IQR to identify and reason about outliers.
A data set of daily step counts has Q1 = 5,200, Q3 = 10,800. (a) Calculate the IQR. (b) Calculate the outlier boundaries (Q1 − 1.5×IQR and Q3 + 1.5×IQR). (c) A value of 25,000 steps is recorded. Is it an outlier? Should it be excluded from the analysis? Justify your answer.
Statistical Literacy — True or False
Circle True or False for each statement about statistical practice.
A larger sample size always eliminates bias
A statistically significant result means the result is practically important
The median is always a better measure of centre than the mean
A survey with 100% response rate guarantees unbiased results
Sampling Methods — Match the Definition
Draw a line from each sampling method to its description.
Evaluating Media Statistics
Critically analyse statistical claims from media sources.
Find or recall a headline that uses statistics (e.g. '9 out of 10 dentists recommend...'). Write the headline and identify two questions you would ask before accepting the claim.
A poll reports: '65% of Australians support the new policy.' What information would you need about the poll before trusting this result?
Explain how a graph with a truncated y-axis can mislead readers. Sketch an example showing how the same data looks very different depending on where the axis starts.
Statistical Bias — Identify the Type
Sort each scenario into the type of bias it demonstrates.
Box Plots and Comparing Distributions
Construct and interpret box plots to compare data sets.
Calculate the five-number summary (min, Q1, median, Q3, max) for this data set: 12, 15, 18, 21, 24, 27, 30, 33, 36. Show all working.
Draw a box plot for the data above. Label all five key values.
A second class has a box plot with median 20, IQR of 8, and a longer upper whisker. Compare the two distributions in terms of centre, spread, and skewness.
Types of Misleading Graphs Encountered
Tally each type of misleading graph technique you identified in media examples.
| Item | Tally | Total |
|---|---|---|
Truncated y-axis | ||
3D distortion | ||
Cherry-picked time period | ||
Missing data labels | ||
Sample size not reported |
Standard Deviation and Spread
Calculate and interpret standard deviation.
Explain what standard deviation measures in plain language. Why is it more useful than the range?
Calculate the mean and standard deviation for: 4, 7, 7, 9, 11. Show all steps.
Class A has mean = 72 and sd = 4. Class B has mean = 72 and sd = 12. What does this tell you about the two classes?
If a new student who scored 90 joins Class A, what effect would this have on the mean and standard deviation?
Designing a Statistical Investigation
Plan a complete statistical investigation from question to conclusion.
Write a research question you could investigate with secondary data available online (e.g. ABS, Bureau of Meteorology).
Describe your data collection plan: source, variables, sample size, and any potential biases.
List three statistical tools (e.g. mean, scatter plot, box plot) you would use to analyse the data and explain why each is appropriate.
Describe how you would present your findings to a non-mathematical audience. What visualisations would you use and why?
Statistical Literacy in the Media
Become a critical consumer of statistics in everyday life.
- 1Collect three news articles this week that include statistics. For each, write one question you would ask about the data before accepting the claim.
- 2Compare how the same statistic is reported by two different news sources. Do they interpret it the same way? Write about any differences.
- 3Watch or read an advertisement that uses statistics. Identify any misleading techniques used. Write a more honest version.
- 4Research a case study where bad statistics led to a wrong conclusion (e.g. early cholesterol research, the MMR vaccine panic). Write a summary.
- 5Interview a family member or friend about a statistic they recently heard. Help them evaluate whether the claim is trustworthy.
Mean, Median, and Mode in Context
Choose and justify the best measure of centre for different data sets.
The weekly wages of 6 employees are: $800, $820, $850, $900, $920, $5,500. Calculate the mean, median, and mode.
Which measure best represents the 'typical' wage? Why does the mean give a misleading picture here?
A real estate agent reports the 'average' house price in a suburb as $1.2 million. Do you think this is a mean or median? Which would you prefer to know as a home buyer?
Margin of Error and Confidence
Interpret margins of error in survey results.
A poll reports: '48% of voters support the policy, with a margin of error of ±3%.' Write the confidence interval this implies.
Another candidate receives 46% support. Can you conclude the first candidate is ahead? Explain.
Explain how increasing the sample size affects the margin of error. What happens to the margin of error if you quadruple the sample size?
Why do political polls sometimes give very different results from the actual election outcome? List three possible reasons.
Statistical Terms — Match to Definition
Match each statistical term to its definition.