How do you read a two-way frequency table and compute joint, marginal, and conditional relative frequencies?
Construct and interpret two-way frequency tables of categorical data, and calculate joint, marginal, and conditional relative frequencies (MA.912.DP.2.4, MA.912.DP.3.1).
A B.E.S.T. Algebra 1 EOC answer on two-way frequency tables (MA.912.DP.2), reading the cells and totals, and computing joint, marginal, and conditional relative frequencies as fractions of the right total.
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What this topic is asking
MA.912.DP.2 asks you to read and interpret a two-way frequency table of categorical data and to compute three kinds of relative frequency: joint, marginal, and conditional. The B.E.S.T. Algebra 1 EOC tests this with table items and multiple choice, and the whole skill is choosing the right total for the denominator.
Reading the table
A two-way table has rows for one category, columns for another, cell counts where they cross, and totals in the margins. For example, rows "plays a sport / does not" and columns "freshman / senior," with each cell the count in that combination, and a grand total in the corner.
The three relative frequencies
| Type | Denominator | Answers |
|---|---|---|
| Joint | grand total | "What fraction are X and Y?" |
| Marginal | grand total (using a margin total) | "What fraction are X overall?" |
| Conditional | a row or column total | "Of the Xs, what fraction are Y?" |
The difference is entirely in the denominator. Joint and marginal both divide by the grand total (a cell vs a margin), while conditional divides by a row or column total because it restricts attention to one group.
How the B.E.S.T. EOC examines this topic
- Table item. Complete a two-way table or read a count from it.
- Number entry. Compute a joint, marginal, or conditional relative frequency.
- Multiple choice. Identify which type of frequency a phrase describes, or interpret a value.
A clarifying idea: every relative-frequency question is "a part over a whole," and the only decision is which whole. "Of everyone" means the grand total; "of the seniors" means the senior total. Pin the denominator first, and the calculation follows.
Why the denominator defines the type
The three frequency types are not different formulas so much as the same fraction with different choices of whole, and the wording dictates that choice. A joint frequency asks how common a specific combination is among everyone, so the whole is the grand total. A marginal frequency asks how common one category is among everyone, again the grand total, but the part is a whole margin rather than a single cell. A conditional frequency narrows the universe to one group first, "given that the person is a senior", so the whole becomes that group's total, and the part is the cell within it. This is why the same cell count, say 8 dog-and-cat owners, yields different relative frequencies depending on whether you divide by 50 (everyone) or 20 (dog owners): the count has not changed, only the population you are comparing it against. Reading the conditioning phrase ("of the...", "given...") tells you exactly which total belongs underneath.
Try this
Q1. A table of 80 students: 24 ride the bus. What is the marginal relative frequency of bus riders? [1 point]
- Cue. .
Q2. Of 40 seniors, 10 are in band. What is the conditional relative frequency of band membership among seniors? [1 point]
- Cue. .
Exam-style practice questions
Practice questions written in the style of FLDOE exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
B.E.S.T. (style)2 marksA survey of 100 students records sport and grade. 30 freshmen play a sport and 20 do not; 35 seniors play a sport and 15 do not. What fraction of students who play a sport are seniors (a conditional relative frequency)?Show worked answer →
The conditional relative frequency is .
"Of students who play a sport" sets the denominator to the total who play a sport: . Of those, are seniors. So the conditional relative frequency is . The key is using the sport-players total, not all 100 students, because the condition restricts the group.
B.E.S.T. (style)1 marksMultiple choice. In a two-way table, what is a marginal relative frequency? (A) a row or column total divided by the grand total (B) a single cell divided by the grand total (C) a cell divided by its row or column total (D) the sum of all cellsShow worked answer →
The correct answer is (A).
A marginal relative frequency is a row or column total (a margin of the table) divided by the grand total, describing one category overall. A joint relative frequency (choice B) is a single cell over the grand total. A conditional relative frequency (choice C) is a cell over its row or column total. The name "marginal" comes from the totals in the table's margins.
Related dot points
- Represent and interpret univariate numerical data using dot plots, histograms, and box plots, and describe the shape (symmetric, skewed left, skewed right) of a distribution (MA.912.DP.1.1, MA.912.DP.1.2).
A B.E.S.T. Algebra 1 EOC answer on data displays (MA.912.DP.1), reading dot plots, histograms, and box plots, the five-number summary, and describing a distribution as symmetric or skewed.
- Calculate and interpret measures of center (mean, median) and spread (range, interquartile range, standard deviation), and choose appropriate measures based on the shape of the distribution and the presence of outliers (MA.912.DP.1.2, MA.912.DP.1.3).
A B.E.S.T. Algebra 1 EOC answer on center and spread (MA.912.DP.1), mean versus median, range and interquartile range, how outliers pull the mean, and choosing the resistant measure.
- Fit a linear function to bivariate numerical data on a scatter plot, interpret the slope and intercept in context, and use the model to make predictions (MA.912.DP.2.4, MA.912.DP.2.5).
A B.E.S.T. Algebra 1 EOC answer on bivariate data (MA.912.DP.2), describing scatter-plot association, fitting a line of best fit, interpreting its slope and intercept, and predicting with interpolation versus extrapolation.
- Interpret the correlation coefficient as a measure of the strength and direction of a linear association, distinguish correlation from causation, and use residuals to assess the fit of a linear model (MA.912.DP.2.6, MA.912.DP.2.8, MA.912.DP.2.9).
A B.E.S.T. Algebra 1 EOC answer on correlation (MA.912.DP.2), reading the correlation coefficient r, why correlation does not prove causation, lurking variables, and using residuals to judge a linear fit.
- Compare key features (intercepts, rate of change, maximums, and minimums) of two functions each represented differently, such as one as an equation and one as a table or graph (MA.912.F.1.5).
A B.E.S.T. Algebra 1 EOC answer on comparing functions (MA.912.F.1.5), extracting slopes, intercepts, and maximums from equations, tables, and graphs, and comparing them when the two functions are shown in different forms.
Sources & how we know this
- B.E.S.T. Mathematics Standards — Florida Department of Education (2020)
- B.E.S.T. Algebra 1 EOC Computer-Based Practice Test — Florida Department of Education (2024)