Data, Statistics, and Probability
What to know
You should compute and interpret mean, median, mode, range, and interquartile range; read dot plots, histograms, box plots, and scatterplots; describe association and line of best fit; distinguish correlation from causation; evaluate sampling methods and sources of bias; and calculate probabilities for simple and compound events, including complements and draws with or without replacement.
Traps
- With an even number of data values, the median is the average of the two middle values.
- The mean is sensitive to outliers; the median is resistant. Questions often ask which measure better describes a skewed data set.
- Probability without replacement changes the denominator on the second draw.
- “At least one” is usually fastest through the complement: 1 − P(none).
- For overlapping events, P(A or B) = P(A) + P(B) − P(A and B); only mutually exclusive events simply add.
- Correlation does not imply causation, and misleading axis scales can exaggerate small differences.
Worked example
A bag holds 3 red and 5 blue marbles. Two are drawn without replacement. Find P(both red). First draw: 3/8. Second draw: 2/7, since one red is gone and 7 marbles remain. Multiply: (3/8)(2/7) = 6/56 = 3/28. Rule of thumb: state whether events are independent or dependent, adjust the denominator for each draw, and multiply along a sequence of events.