Data Analysis, Statistics, and Probability
Data Analysis, Statistics, and Probability - what the exam tests
This domain asks you to summarize data, read graphs and tables accurately, compare distributions, and compute probabilities. Expect mean, median, mode, range, weighted averages, qualitative standard deviation, basic counting, and scatterplot interpretation.
Core rules
- Center: mean = sum ÷ count; median = middle value after ordering; mode = most frequent value.
- Weighted mean: (Σ value × weight) ÷ (Σ weights). Use it for course grades and combined groups.
- Spread: range = maximum − minimum. Standard deviation measures typical distance from the mean; adding a constant to every value shifts the mean but leaves the standard deviation unchanged, while multiplying every value by k multiplies the standard deviation by |k|.
- Probability: P(event) = favorable outcomes ÷ total outcomes. For independent events, P(A and B) = P(A)·P(B). For mutually exclusive events, P(A or B) = P(A) + P(B). The complement rule is P(not A) = 1 − P(A).
- Counting: multiply choices for sequential decisions; use combinations for unordered selections and permutations for ordered arrangements.
- Scatterplots: describe direction, strength, and form; a line of best fit supports prediction only within the observed range.
Worked example
For 3, 7, 7, 9, 14: the mean is 40 ÷ 5 = 8; the median is 7; the mode is 7; the range is 11. If 2 is added to every value, the new mean is 10 and the median is 9, but the range stays 11 and the standard deviation is unchanged.
Traps that cost marks
- Taking a median without ordering the data.
- Mixing up 'and' (multiply for independent events) with 'or' (add for mutually exclusive events).
- Forgetting that drawing without replacement changes the denominator.
- Reading a graph whose axis does not start at zero as if it did.
- Treating correlation as proof of causation.