Data Analysis, Statistics and Probability
This domain tests bivariate data and categorical data: reading scatter plots, describing association, using a line of best fit, and analyzing two-way tables with relative frequencies. Probability questions may ask for simple probabilities from a table or sample space.
Scatter plots
A scatter plot displays paired numerical data. Describe the association by direction (positive, negative, or none), form (linear or nonlinear), and strength (strong or weak). Look for clusters and outliers. A positive association means that as x increases, y tends to increase; a negative association means y tends to decrease. Association does not prove causation.
Line of best fit
A line of best fit models the trend. Its slope describes the predicted change in y for each one-unit increase in x, with units. Its y-intercept is the predicted y when x = 0, which may or may not make sense in context. Use the line to predict within the observed data range (interpolation); predictions far outside that range (extrapolation) are less reliable.
Two-way tables
A two-way table organizes two categorical variables. Joint relative frequency uses the grand total as the denominator. Marginal relative frequency uses a row or column total over the grand total. Conditional relative frequency uses a row or column total as the denominator and answers “given” questions. Always identify the given group first.
Probability
Probability of an event = number of favorable outcomes ÷ total number of equally likely outcomes. Probabilities range from 0 to 1. For two independent events, multiply their probabilities: P(A and B) = P(A)·P(B).
Worked example
A two-way table shows 30 seventh graders and 30 eighth graders. Of the seventh graders, 18 have a pet; of the eighth graders, 24 have a pet. The conditional relative frequency of having a pet given eighth grade is 24/30 = 0.80. The joint relative frequency of being an eighth grader with a pet is 24/60 = 0.40. These are different questions because the denominators differ.
Traps that cost marks
- Using the grand total when the question says “given” a row or column.
- Confusing joint and conditional relative frequencies.
- Describing association as causation.
- Extrapolating far beyond the data and treating the prediction as exact.
- Ignoring an outlier when describing the line of best fit.
- Forgetting that slope has units and interpreting it without them.