Course outline
Module 1
Module 1: Why Data Matters
Why Data Matters
Knowledge check
Q1. Which of the following best describes why data matters in decision-making?
- A. Data replaces the need for human judgment entirely
- B. Data provides evidence that can help reduce guesswork and support better-informed decisions
- C. Data is only useful for large corporations and governments
- D. Data guarantees that the correct decision will always be made
Q2. A shop owner notices sales rose after a new display was installed. What is the most important next step before concluding the display caused the increase?
- A. Immediately install displays in all other shops
- B. Check whether other factors, such as seasonality or a promotion, could explain the rise
- C. Stop collecting sales data to avoid bias
- D. Assume the increase is permanent without further evidence
Q3. What is a 'sample' in statistics?
- A. The entire group you want to learn about
- B. A free product given to customers
- C. A subset of the population that is observed and measured
- D. A mathematical formula used to calculate averages
Q4. Why might a survey of 50 customers from a single store give misleading results about all customers of a company?
- A. Surveys always produce false answers
- B. The sample may not represent the wider population of customers across all locations
- C. Fifty is too large a number to be useful
- D. Customers never tell the truth in surveys
Q5. Which type of data is numerical and can be measured, such as height or temperature?
- A. Qualitative data
- B. Categorical data
- C. Quantitative data
- D. Anecdotal data
Module 2
Module 2: Describing Data with Averages and Spread
Describing Data with Averages and Spread
Knowledge check
Q1. Which measure of average is found by adding all the values together and dividing by the number of values?
- A. The median
- B. The mode
- C. The mean ✓
- D. The range
Why: The mean is calculated by summing all values and dividing by how many values there are. The median is the middle value, the mode is the most frequent value, and the range is a measure of spread, not an average.
Q2. What is the median of the data set: 3, 7, 1, 9, 5?
Why: First arrange the values in order: 1, 3, 5, 7, 9. The middle value is 5, which is the median. Adding them gives 25, and dividing by 5 gives a mean of 5, but the median is simply the middle value.
Q3. What is the range of the data set: 12, 4, 18, 9, 15?
- A. 6
- B. 14 ✓
- C. 11.6
- D. 18
Why: The range is the largest value minus the smallest value. Here, 18 minus 4 equals 14. It measures how spread out the data is across its full extent.
Q4. Which value is the mode of the data set: 2, 5, 5, 8, 9, 5, 2?
Why: The mode is the value that appears most often. The number 5 appears three times, more than any other value, so 5 is the mode.
Q5. A data set has a mean of 10 and contains 4 values. What is the total of all the values?
- A. 2.5
- B. 14
- C. 40 ✓
- D. 400
Why: Since mean equals total divided by the number of values, the total equals the mean multiplied by the number of values. So 10 multiplied by 4 gives 40.
Module 3
Module 3: Seeing Patterns in Charts
Seeing Patterns in Charts
Knowledge check
Q1. A bar chart shows monthly sales for a shop, with bars for January through June. The bars are 40, 42, 41, 43, 42, and 44 units. What is the best description of the overall trend?
- A. Sales are falling steadily over the six months
- B. Sales are rising slowly with small ups and downs ✓
- C. Sales jumped sharply in March and then dropped
- D. Sales stayed exactly the same every month
Why: The values go up overall from 40 to 44, but with small dips such as 42 to 41 and 43 to 42. A slow rise with minor fluctuations best describes this pattern.
Q2. A line chart's vertical axis starts at 95 instead of 0, so a change from 96 to 100 looks very dramatic. What is the main concern with this design?
- A. Line charts should never show numbers above 90
- B. The truncated axis can exaggerate the size of the change visually ✓
- C. The chart cannot show percentages when the axis does not start at zero
- D. The chart is automatically inaccurate and must be discarded
Why: Starting the axis at a non-zero value compresses the scale and can make small differences look large. The data is not wrong, but the visual impression can mislead the viewer.
Q3. A scatter plot shows hours studied on the horizontal axis and exam scores on the vertical axis. The points rise from the bottom left to the top right. What does this suggest?
- A. Studying more hours causes exam scores to drop
- B. There is a positive association between hours studied and exam scores ✓
- C. There is no relationship between the two variables
- D. Exam scores are always higher than hours studied
Why: When points rise from left to right, the two variables tend to increase together, which is a positive association. This does not by itself prove that studying causes higher scores.
Q4. A pie chart shows that 60% of survey respondents chose option X. A student says this means 60 out of every 100 people in the country chose X. What is the key flaw in this reasoning?
- A. Pie charts cannot show percentages
- B. The student ignored that the survey may not represent the whole country ✓
- C. Sixty percent is always a mistake and should be 50%
- D. Pie charts only work with three categories
Why: A chart describes the survey sample, not automatically the whole population. Conclusions about the country require knowing how representative the sample was.
Q5. A chart shows average daily temperature by month, with a smooth curve that peaks in July and dips in January. What type of pattern is this?
- A. A random pattern with no structure
- B. A seasonal pattern that repeats across the year ✓
- C. An outlier that should be removed
- D. A pattern caused by errors in measurement
Why: Values that rise and fall in a regular cycle tied to the calendar, like temperatures over a year, form a seasonal pattern. Recognizing this helps you expect similar cycles in future years.
Module 4
Module 4: Chance, Probability, and Everyday Risk
Chance, Probability, and Everyday Risk
Knowledge check
Q1. A fair coin is flipped and lands heads 5 times in a row. What is the probability that the next flip is heads?
- A. Less than 50%, because tails is due
- B. Exactly 50% ✓
- C. Greater than 50%, because heads is on a streak
- D. Close to 0%
Why: Each coin flip is independent. Past outcomes do not change the probability of future flips, so the chance of heads remains 50%. The belief that tails is 'due' is the gambler's fallacy.
Q2. A test for a rare disease is 99% accurate, and 1 in 1,000 people have the disease. If a person tests positive, which statement is most accurate?
- A. They almost certainly have the disease, about 99% chance
- B. They have a 1% chance of having the disease
- C. They have roughly a 9% chance of having the disease ✓
- D. They have a 50% chance of having the disease
Why: Out of 100,000 people, about 100 have the disease and nearly all test positive. About 1% of the 99,900 healthy people (around 999) also test positive falsely. So roughly 1,099 test positive, and only about 100 of those are truly sick, giving roughly a 9% chance.
Q3. If you roll two fair six-sided dice, what is the probability that the total is 7?
- A. 1/12
- B. 1/6 ✓
- C. 1/36
- D. 1/3
Why: There are 36 equally likely outcomes. Six of them sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). So the probability is 6/36, which equals 1/6.
Q4. Which of these events is the least likely to happen in a single day for a typical person?
- A. Being struck by lightning
- B. Being in a car accident that causes injury
- C. Winning a major national lottery jackpot ✓
- D. Flipping a coin and getting heads
Why: Winning a major lottery jackpot has odds on the order of one in tens or hundreds of millions per ticket. Lightning strikes, injurious car accidents, and a coin landing heads are all far more probable events over a day for most people.
Q5. A study finds that people who drink coffee have a higher rate of a certain illness. What is the most cautious conclusion?
- A. Coffee causes the illness
- B. Coffee cures the illness
- C. Coffee and the illness are associated, but the study alone does not prove coffee causes it ✓
- D. The study proves there is no link between coffee and the illness
Why: Observational studies reveal correlation, not causation. Confounding factors such as smoking, diet, or stress could explain the association. Claiming causation without experimental evidence, or dismissing the link entirely, goes beyond what the data show.
Module 5
Module 5: Samples and Why They Can Mislead
Samples and Why They Can Mislead
Knowledge check
Q1. A researcher wants to estimate the average monthly spending of all households in a city. Which sampling approach is most likely to produce a representative sample?
- A. Surveying only households in the wealthiest neighbourhood because they are easiest to reach
- B. Randomly selecting households from a complete list of all households in the city ✓
- C. Asking shoppers leaving the largest shopping mall to report their spending
- D. Posting an online survey and using all responses that come back
Why: Random selection from a complete list gives every household an equal chance of being included, which reduces systematic bias and makes the sample more likely to reflect the whole population. The other options all favour certain types of households and so distort the estimate.
Q2. A magazine asks its readers to mail back a postcard stating whether they support a new policy. Why are the results likely to mislead?
- A. Postcards are too cheap to produce accurately
- B. Only people with strong feelings are likely to respond, so the sample is self-selected ✓
- C. Readers always agree with the magazine's editorial position
- D. The sample size is always too small to produce any result
Why: This is a self-selection or voluntary response bias. People who feel strongly, or who are motivated by the issue, are more likely to bother responding, so the results may not reflect the opinions of the wider readership or public.
Q3. A study of a sample of 50 people finds an average height that differs from the national average. Which factor most directly affects how much the sample average might differ from the true population average by chance alone?
- A. The colour of the researchers' clothing
- B. The sample size, with larger samples generally giving more precise estimates ✓
- C. The day of the week the data was collected
- D. The number of words in the study report
Why: Sampling variability decreases as sample size increases, so larger samples typically yield estimates closer to the true population value. A sample of 50 can easily differ from the national average purely by chance, which is why sample size matters.
Q4. A health website reports that a new diet helped the 12 people who completed a trial, but 8 of the original 20 participants dropped out before the end. What is the main concern with reporting only the 12 completers?
- A. Twelve is an even number, which makes results unreliable
- B. The dropouts may differ systematically from completers, so the results may be biased ✓
- C. Diets never work for more than a few people
- D. The trial must have been conducted incorrectly from the start
Why: This is attrition bias. If those who left the trial did so because the diet was unpleasant or ineffective, then analysing only completers gives an overly positive picture. The remaining group is no longer comparable to the original group.
Q5. A city council asks residents to call a phone-in line to say whether they want a new park. Over 500 calls are received, all in favour. Why should the council be cautious about concluding that most residents want the park?
- A. Phone calls are always more accurate than other methods
- B. A large number of responses does not fix a biased sample, since the callers may not represent all residents ✓
- C. Residents never want new parks
- D. The council should ignore all responses that favour the park
Why: Sample size cannot compensate for a biased selection method. Those who choose to call are likely more motivated and not representative of all residents, so 500 supportive callers may still give a misleading picture of overall opinion.
Module 6
Module 6: Correlation Is Not Causation
Correlation Is Not Causation
Knowledge check
Q1. A study finds that people who own more books tend to live longer. Which conclusion is best supported by this finding alone?
- A. Owning more books causes people to live longer.
- B. Owning books and longer life are associated, but the study alone does not show that one causes the other. ✓
- C. Reading books makes people healthier, which extends their lives.
- D. Book owners are wealthier, and wealth directly causes longevity.
Why: The study shows a correlation between book ownership and lifespan. Correlation alone cannot establish causation, so the best conclusion is that the two are associated without proof that one causes the other.
Q2. Ice cream sales and drowning deaths both rise during summer. What is the most likely explanation for this correlation?
- A. Eating ice cream makes people more likely to drown.
- B. Drowning deaths cause ice cream sales to increase.
- C. A third factor, hot weather, increases both ice cream sales and swimming, which leads to more drownings. ✓
- D. The correlation is a coincidence with no underlying cause at all.
Why: This is a classic confounding variable example. Hot weather drives both ice cream consumption and swimming, so it links the two outcomes without either causing the other.
Q3. Which of the following is the clearest way to test whether a new teaching method causes better exam scores?
- A. Ask students at the end of the year whether they liked the method.
- B. Compare exam scores of students who chose the method with those who did not.
- C. Randomly assign students to either the new method or the usual method and compare results. ✓
- D. Look at whether the best teachers happen to use the new method.
Why: Random assignment spreads other factors, such as motivation or prior ability, evenly across groups. This makes it possible to attribute any difference in scores to the teaching method itself.
Q4. A researcher notices that cities with more police officers have higher crime rates. What is the most sensible next step before concluding that police increase crime?
- A. Conclude that police officers are causing crime and reduce their numbers.
- B. Consider reverse causation and confounders, such as higher-crime cities choosing to hire more police. ✓
- C. Assume the data is wrong because the result seems unlikely.
- D. Stop analysing the data because correlations are always meaningless.
Why: The relationship could run in reverse, with high crime prompting more police hiring, or be driven by a confounder such as city size. Good analysis checks these alternative explanations before drawing causal conclusions.
Q5. Which statement correctly describes the difference between correlation and causation?
- A. Correlation and causation mean exactly the same thing in statistics.
- B. Correlation means two variables move together, while causation means a change in one directly produces a change in the other. ✓
- C. Causation can be proven from correlation coefficients alone.
- D. Correlation shows causation whenever the sample size is large enough.
Why: Correlation describes a pattern where two variables vary together, while causation means one variable actually brings about changes in the other. A strong correlation does not by itself establish causation, regardless of sample size.
Module 7
Module 7: Spotting Statistics in the News
Spotting Statistics in the News
Knowledge check
Q1. A news headline says 'Coffee drinkers are 50% less likely to develop the disease.' The study found the disease rate fell from 2 in 1,000 people to 1 in 1,000 people. What is the most important context missing from the headline?
- A. The name of the researchers who conducted the study
- B. That the absolute risk dropped by only 1 in 1,000, a much smaller change than the 50% relative figure suggests ✓
- C. The color of the chart used in the original report
- D. Whether the newspaper printed the story on the front page
Why: Relative risk reductions can sound dramatic while the absolute change is tiny. Going from 2 in 1,000 to 1 in 1,000 is a 50% relative drop but only a 0.1 percentage point absolute drop. Always check the baseline numbers.
Q2. A survey of 200 people finds that 62% prefer Brand X, with a stated margin of error of plus or minus 3 percentage points. A journalist writes that 'Brand X is clearly the public favorite over Brand Y, which got 58%.' What is the best critique?
- A. The survey sample is too large to be reliable
- B. The 4-point gap is within the margin of error, so the difference may not be real ✓
- C. Percentages should never be reported in news articles
- D. The journalist should have used a pie chart instead
Why: With a margin of error of plus or minus 3 points, Brand X could be anywhere from about 59% to 65%, and Brand Y from about 55% to 61%. These ranges overlap, so the claim that Brand X is clearly ahead is not supported by the data.
Q3. A news story reports: 'Cities that added more bike lanes saw crime rise. Therefore, bike lanes cause crime.' Which statistical principle does this claim most clearly ignore?
- A. Sample size calculation
- B. Regression to the mean
- C. Correlation does not imply causation ✓
- D. Standard deviation
Why: Two things moving together does not mean one causes the other. Both bike lane construction and crime could be influenced by a third factor, such as city size or population density, or the relationship could be coincidental.
Q4. A headline states: 'Study finds eating chocolate boosts Nobel Prize odds.' The study was based on a survey of 23 Nobel laureates who were asked about their diets. What is the most serious weakness?
- A. The study was published in a journal with a blue cover
- B. The sample is very small and self-selected, so the result may easily be due to chance or bias ✓
- C. Chocolate is not a food
- D. Nobel Prizes are awarded only in Sweden
Why: A sample of 23 people is too small to draw reliable conclusions, and the findings may reflect random variation. Surveys of this kind also rely on self-reported data, which can be inaccurate, and there is no control group for comparison.
Q5. A news report says 'Average home prices rose to $450,000 this year, up from $400,000 last year.' A reader notices the report did not mention that a few extremely expensive luxury sales were included in the average. What concept should the reader be most concerned about?
- A. Outliers skewing the mean, which may make the typical home price look higher than it really is ✓
- B. The font used for the report
- C. The number of pages in the housing report
- D. The time of day the report was published
Why: The mean is sensitive to extreme values. A few very expensive sales can pull the average upward, so the median price, which is less affected by outliers, may give a more accurate picture of what a typical buyer pays.