Data Analysis, Statistics, and Probability
The Data Analysis, Statistics, and Probability domain tests whether you can read and critique data displays, choose and interpret measures of center and spread, judge sampling methods, and compute probabilities for simple, compound, and dependent events - including recognizing misleading presentations of data.
Describing data
- The mean is the sum divided by the count and is pulled strongly by outliers; the median is resistant to them.
- With an even number of values, the median is the average of the two middle values.
- Range = maximum − minimum; interquartile range = Q3 − Q1 and describes the middle half of the data.
Probability
- For equally likely outcomes, P(event) = favorable outcomes ÷ total outcomes; every probability lies between 0 and 1.
- For independent events, multiply: P(A and B) = P(A)·P(B).
- Drawing without replacement changes the denominator and the count of the drawn category on the second draw.
Worked example
A bag holds 5 red and 3 blue marbles, 8 total. Two are drawn without replacement. P(both red) = 5/8 × 4/7 = 20/56 = 5/14 ≈ 0.357. With replacement, the probability would be 5/8 × 5/8 = 25/64 ≈ 0.391. The gap comes from the reduced total (8 → 7) and the reduced number of red marbles (5 → 4) after the first draw.
Sampling and inference
- Random sampling supports generalization to the population; volunteer and convenience samples generally do not.
- A sample statistic estimates a population parameter, so results vary from sample to sample.
Traps that cost marks
- Reading a bar graph with a truncated vertical axis as evidence of a large effect.
- Treating "or" as multiplication instead of using P(A or B) = P(A) + P(B) − P(A and B).
- Reporting the mean for clearly skewed data where the median is the better summary.
- Assuming a correlation shown in a scatterplot proves causation.