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How do you read a two-way frequency table and compute joint, marginal, and conditional relative frequencies?

Summarize two-variable categorical data in two-way tables and interpret joint, marginal, and conditional relative frequencies (NC.M1.S-ID.5).

An NC Math 1 EOC answer on two-way frequency tables (NC.M1.S-ID.5): reading counts, computing joint, marginal, and conditional relative frequencies, and recognizing possible association between two categorical variables.

Generated by Claude Opus 4.811 min answer

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  1. What this topic is asking
  2. The three kinds of frequency
  3. Reading a two-way table
  4. Recognizing association
  5. How the NC Math 1 EOC examines this topic
  6. Why conditional frequencies reveal relationships
  7. Try this

What this topic is asking

NC.M1.S-ID.5 asks you to summarize two-variable categorical data in a two-way frequency table and interpret joint, marginal, and conditional relative frequencies, recognizing possible association between the variables. This is the categorical counterpart to scatter plots for numerical data.

The three kinds of frequency

The names tell you where in the table to look.

The phrase "of those who..." is the signal for a conditional frequency: it restricts the denominator to a subgroup.

Reading a two-way table

Recognizing association

Two variables may be associated if a conditional frequency differs noticeably across groups. If 67%67\% of coffee drinkers are morning people but only 25%25\% of non-coffee drinkers are, the difference suggests an association between coffee drinking and being a morning person. Equal conditional frequencies suggest no association.

How the NC Math 1 EOC examines this topic

  • Gridded response. Compute a joint, marginal, or conditional relative frequency as a fraction or percent.
  • Multiple choice. Identify the type of frequency, or whether the data suggests association.
  • Technology-enhanced. Fill in a two-way table, or select the correct conditional statement.

Two-way tables handle categorical pairs, while scatter plots handle numerical pairs; both are about relationships between two variables, a theme continued in correlation and causation.

Why conditional frequencies reveal relationships

A joint or marginal frequency describes the whole group, but a conditional frequency zooms into a subgroup and asks how the other variable behaves there. That zoom is what exposes a relationship: if knowing one category changes the likelihood of the other, the variables are associated. This is exactly why the EOC distinguishes the three frequency types so carefully, they answer different questions. "What fraction of everyone drinks coffee and is a morning person" (joint) is not the same as "what fraction of coffee drinkers are morning people" (conditional). Misreading "of those who" as a fraction of the whole is the single most common error, and getting the denominator right is the heart of S-ID.5.

Try this

Q1. A table of 8080 people has 3030 who own a pet and also exercise. What is this joint relative frequency? [1 point]

  • Cue. 3080=37.5%\frac{30}{80} = 37.5\% of everyone.

Q2. Of 4040 pet owners, 3030 exercise. What is the conditional relative frequency? [2 points]

  • Cue. Condition on the 4040 owners: 3040=75%\frac{30}{40} = 75\%.

Exam-style practice questions

Practice questions written in the style of NCDPI exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

NC Math 1 EOC (style)2 marksIn a survey of 200200 students, 120120 like pizza and of those 8080 also play sports. What fraction of pizza-likers play sports?
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The conditional relative frequency is 80120=23\frac{80}{120} = \frac{2}{3}, about 67%67\%.

A conditional relative frequency restricts to a subgroup. Here we condition on the 120120 pizza-likers and ask how many play sports: 80120=23≈67%\frac{80}{120} = \frac{2}{3} \approx 67\%. Note this differs from the joint frequency 80200=40%\frac{80}{200} = 40\% (out of everyone). Reading "of those" as a conditional is the S-ID.5 skill.

NC Math 1 EOC (style)1 marksIn a two-way table, the row and column totals in the margins are called: (A) joint frequencies (B) marginal frequencies (C) conditional frequencies (D) outliers
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The correct answer is (B), marginal frequencies.

The totals in the margins (the bottom row and right column) are the marginal frequencies, giving the total for each category of one variable. A joint frequency is a single inner cell; a conditional frequency divides within a row or column. The names come from where the numbers sit in the table.

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