Statistics

Why is it important to think about variation rather than just single numbers when looking at data? How do different shapes of distributions—like symmetric, skewed, or multi-peaked—tell different stories? What kinds of questions should we ask before trusting a dataset as representative? How can visual tools like histograms or box plots make variation easier to grasp? Can you think of a time when ignoring variation led to a misleading conclusion?

How do mean, median, and mode each capture different aspects of what is 'typical' in a dataset? When might the median be more informative than the mean, and why? What do measures of spread like range or standard deviation add to our understanding of data? How can two groups have the same average but still be very different in reality? Can you think of a news story where a single summary number oversimplified a complex situation?

What does it mean for two variables to be correlated, and what are the limits of that idea? Why is 'correlation is not causation' such an important warning in interpreting data? What kinds of evidence strengthen the case that one factor might actually cause changes in another? How can confounding variables create illusions of cause where none exists? Can you recall an example where people blamed the wrong cause because of a misunderstood correlation?

What is the difference between an observational study and a controlled experiment? How can sampling methods introduce bias into a study, even if the math afterward is correct? What ethical issues arise when designing experiments on humans or communities? How do blinding, randomization, and control groups help produce more reliable results? What questions should an informed citizen ask when reading about a new study in the news?

How can statistics help us make reasonable claims about a whole population based on limited samples? What is the difference between a point estimate and a confidence interval? Why do misunderstandings about p-values cause so much confusion in scientific reporting? How should we communicate uncertainty honestly without paralyzing decision-making? Can you think of a policy or personal decision where acknowledging uncertainty would change the conversation?

What are some common ways that statistics or graphs can be used to mislead rather than inform? How can selective reporting or 'p-hacking' distort the scientific record? What responsibilities do journalists and experts have when presenting numbers to the public? How can ordinary people protect themselves from being fooled by bad or biased statistics? Can you think of an example where better statistical literacy might have changed a major public debate?