Probabilistic and Statistical Reasoning: Data, Probability, and Inference
Probabilistic and Statistical Reasoning covers summarizing data, reading graphs and tables, computing simple probabilities, and judging whether a study supports its conclusion.
For a data set, know four summaries: mean (sum ÷ count), median (middle value of an ordered list), mode (most frequent), and range (max − min). With an even number of values, the median is the average of the two middle values. A weighted mean - used for GPA and course grades - multiplies each value by its weight, sums, then divides by total weight. Outliers pull the mean far more than the median, so when data are skewed the median better describes a typical value.
Probability of a single event = favorable outcomes ÷ total outcomes, and P(not A) = 1 − P(A). For two independent events, multiply. For "without replacement" draws, the denominator shrinks after the first pick. Two-way tables are a favorite: a conditional probability such as "given that the student is a sophomore, what is P(prefers online)?" restricts the denominator to the sophomore row only.
Traps to watch. Forgetting to sort data before finding the median; dividing by the wrong total in a two-way table; treating correlated variables as causally linked; and extrapolating a line of fit far beyond the observed data.
Worked example. For 4, 7, 7, 9, 13: mean = 40 ÷ 5 = 8; the ordered middle value is 7, so median = 7; mode = 7; range = 13 − 4 = 9. The mean exceeds the median, hinting at right skew from the 13.