Statistics and Probability
Statistics and Probability on NYS mathematics exams tests data summary, displays, association, sampling, probability rules, and normal models. Questions often ask you to interpret a statistic in context, not just compute it.
Core rules and concepts
- Mean is affected by outliers; median and IQR are resistant. Standard deviation measures spread around the mean.
- Scatterplots show direction, strength, and form. The correlation coefficient r is between -1 and 1; regression lines predict y from x, and residuals are actual minus predicted. Correlation does not prove causation.
- Probability is between 0 and 1; complement P(not A)=1-P(A). For conditional probability, P(A|B)=P(A and B)/P(B).
- Events are independent when P(A and B)=P(A)P(B). Mutually exclusive events cannot occur together.
- Normal data roughly follow 68-95-99.7 within 1, 2, 3 standard deviations; z=(x-mean)/standard deviation.
Worked example
A two-way table shows 100 students: 40 play a sport, and 25 of those 40 also play an instrument. Find P(instrument | sport). The condition restricts the sample space to the 40 sport players, so the denominator is 40, not 100: P=25/40=0.625. Reasoning: “given sport” means look only at the sport row; the 25 instrument players inside that row are the favorable cases.
Traps that cost marks
- Using the grand total as the denominator in a conditional probability.
- Confusing independent events with mutually exclusive events.
- Treating a strong correlation as evidence of causation.
- Extrapolating a regression line far beyond the data or ignoring outliers.