Statistics & Probability
Statistics & Probability on the Regents Algebra I exam asks you to summarize and compare data displays, interpret scatter plots and lines of best fit, read two-way frequency tables, and compute probabilities. The emphasis is on explaining what a number means in context. You should be comfortable with dot plots, histograms, box plots, and the relationship between frequency and relative frequency.
Core rules
- Measures of center and spread: the median is the middle value; the interquartile range is Q3−Q1. The mean is affected by outliers more than the median.
- A line of best fit models a scatter plot. Its slope gives the predicted change in y per one-unit increase in x; its y-intercept gives the predicted y when x=0, but only interpret it if x=0 is meaningful.
- Correlation measures the strength and direction of a linear association. Correlation does not imply causation, and a fitted line should not be extrapolated far beyond the data.
- In a two-way table, a conditional probability uses a row or column total as the denominator, not the grand total. P(A|B)=P(A and B)/P(B).
Worked example
In a survey of 100 students, 40 take art and 60 do not. Of the art students, 25 take music; of the non-art students, 15 take music. Find P(music | art). Restrict to the art row: 25 of 40 take music, so P=25/40=0.625. The reasoning is that the condition 'art' fixes the denominator at 40; using 100 would answer a different question.
Traps
Do not use the grand total when a conditional probability calls for a row or column total. Do not treat a strong correlation as proof of cause. Do not read a residual as the data value; it is actual minus predicted. When comparing distributions, report both center and spread rather than only the mean.