Introductory Statistics

What you'll learn

• Distinguish populations from samples and parameters from statistics, classify variables, and ask the questions that expose misleading numbers and protect the privacy of the people behind data.
• Identify levels of measurement, distinguish observational studies from experiments, choose random sampling designs, recognize sources of bias, write neutral survey questions and apply control, randomization and replication.
• Choose and read graphs for categorical and quantitative data, describe distributions by shape, center, spread and outliers, read time series, and recognize misleading graphs.
• Compute and interpret the mean, median, quartiles, interquartile range, standard deviation, five-number summary, boxplots, z-scores and weighted means, including price indexes such as the CPI.
• Use the normal distribution and the 68–95–99.7 rule to find proportions and percentiles, and judge when a normal model is appropriate.
• Describe relationships with scatterplots and correlation, fit and interpret least-squares regression lines, residuals and r squared, avoid extrapolation, and explain why association is not causation, including Simpson's paradox.
• Apply the rules of probability, conditional probability, independence and Bayes' theorem, including base rates in medical testing, and count outcomes to find probabilities such as lottery odds.
• Find the expected value and standard deviation of discrete random variables, apply the binomial distribution and its normal approximation, and use expected values in insurance and gambling.
• Explain sampling distributions, unbiasedness and the square-root law, and use the central limit theorem for sample means and proportions.
• Construct and interpret confidence intervals for proportions and means, explain margins of error in polls, and choose sample sizes for a desired precision.
• Carry out and interpret hypothesis tests for a proportion and a mean, explain p-values, Type I and Type II errors and power, and distinguish statistical significance from practical importance.
• Compare two proportions, two means and paired data, use chi-square tests for categorical data, choose an appropriate procedure, and use and communicate statistics responsibly, including in A/B tests.