Data Analysis, Statistics, and Probability
Data Analysis, Statistics, and Probability covers summarizing a data set, reading displays such as histograms and box plots, interpreting scatterplots and lines of best fit, and computing probabilities for single and compound events.
Core rules
- Mean = sum ÷ count. With an even count, the median is the average of the two middle values after ordering.
- Outliers pull the mean but barely move the median, so the median is described as resistant.
- Weighted mean = Σ(value × weight) ÷ Σweights.
- Probability of an event = favorable outcomes ÷ total equally likely outcomes, always between 0 and 1, with P(not A) = 1 − P(A).
- Independent events: P(A and B) = P(A) × P(B). For draws without replacement, reduce both the numerator and the denominator after the first draw.
- P(A or B) = P(A) + P(B) − P(A and B).
Worked example
Five test scores average 82. What sixth score raises the mean to 85? Work with totals rather than averaging averages. Current total = 5 × 82 = 410. Needed total = 6 × 85 = 510. Sixth score = 510 − 410 = 100. For a probability companion: from 3 red and 5 blue marbles, two drawn without replacement, P(both red) = 3/8 × 2/7 = 3/28, because the second draw sees only 7 marbles and 2 reds.
Traps that cost marks
- Treating "and" and "or" as interchangeable, or omitting the overlap when events are not mutually exclusive.
- Computing a without-replacement draw as if the first marble were put back.
- Judging spread by comparing means; variability needs range, interquartile range, or standard deviation.
- Reading a bar graph whose vertical axis does not start at zero and drawing a false conclusion about relative size.
- Reporting the mean of a skewed data set as typical without noting the outlier's effect.