TNReady Algebra I: a complete guide to statistics and probability

What this category demands

This guide covers the Statistics and Probability reporting category (TN domain A1.S.ID, Interpreting Categorical and Quantitative Data), about 15 to 18 percent of the TNReady Algebra I test. It is a reliable point block built on reading data, not heavy computation. Each dot-point page has its own practice: representing data, center and spread, two-way frequency tables, scatter plots and linear models, and correlation and causation.

Representing and summarizing one variable

Single-variable data is shown with a dot plot (a dot per value), a histogram (bars by binned frequency, showing shape), or a box plot (the five-number summary: min, $Q_1$, median, $Q_3$, max). Center is the mean or median; spread is the range, IQR ($Q_3 - Q_1$), or standard deviation. The rule for choosing: symmetric data uses the mean and standard deviation; skewed data or data with outliers uses the median and IQR, since outliers distort the mean but not the median.

Two-way frequency tables

For two categorical variables, a two-way table holds joint frequencies (cells), marginal totals (row and column sums), and the grand total. A conditional relative frequency divides a cell by its row or column total ("of those who ..."), while a joint relative frequency divides by the grand total. The conditioning phrase fixes the denominator.

Scatter plots, models, and causation

For two quantitative variables, a scatter plot shows the association (direction, form, strength). A line of best fit $y = mx + b$ summarizes a linear pattern: the slope is the predicted change in $y$ per unit of $x$ (a rate), and the intercept is the predicted $y$ at $x = 0$. The correlation coefficient $r$ (from $-1$ to $1$) gives direction (sign) and strength (magnitude). Crucially, a strong correlation does not prove causation, a lurking variable may drive both.

How this category is examined

• Multiple choice and multiple select. Compute the IQR or a relative frequency, name a shape, interpret $r$, or choose a valid causal conclusion.
• Numeric response. Find a mean, median, IQR, conditional frequency, or a prediction from a model.
• Drag and drop / inline choice. Match displays, complete tables, or finish a statement about a relationship.

Check your knowledge

Work these as you would for credit on the EOC.

1. A box plot has $Q_1 = 12$, $Q_3 = 30$. Find the IQR. (1 point)
2. Find the median of $5, 9, 11, 14, 90$, and explain why it beats the mean here. (2 points)
3. A histogram trails off to the right. Name the shape. (1 point)
4. In a two-way table, $40$ of $60$ teens own a bike and $25$ of those bike to school. What fraction of bike owners bike to school? (1 point)
5. A model is $y = 5x + 20$ for ads ($x$) versus sales ($y$). Interpret the slope. (1 point)
6. Using $y = 5x + 20$, predict sales for $10$ ads. (1 point)
7. A data set has $r = -0.92$. Describe the relationship. (1 point)
8. Sales of sunscreen and sunglasses are correlated. Give the likely lurking variable. (1 point)