AP Statistics · Unit 1 · Topic 1.3

Frequency Tables Study Lab

A categorical variable is summarized by how many individuals fall in each category (the frequency) and what fraction of the total that is (the relative frequency). Edit the table, watch every proportion update, and practice the backward problems AP likes to ask.

1. Build a frequency table

A frequency table lists each category with its count. Divide each count by the total to get the relative frequency.

relative frequency = count ÷ total percent = relative frequency × 100

Preset data sets

Edit the categories and counts

Type in the count column. Everything else updates.

Relative frequencies

Total n

Mode (most common)

Proportion in the mode

Sum of relative frequencies

Show your work

Practice: work backward from a table

AP questions often give percents and ask for counts, or leave one cell blank. Solve, then check.

Your answer

2. Key ideas

Counts

Frequency table

Lists each category and how many individuals are in it. The counts add to the total number of individuals, n.

Proportions

Relative frequency

Count ÷ total. It can be written as a decimal (0.36) or percent (36%). The relative frequencies of all the categories add to 1, apart from rounding.

Compare

Why proportions?

Proportions put groups of different sizes on the same scale. 60 out of 100 and 60 out of 400 are very different results.

Center

Mode

The category with the highest frequency. It is the only measure of center that makes sense for categorical data.

Backward

From percent to count

Count = proportion × total, and total = count ÷ proportion. Many AP questions give you two of the three.

Context

Report in words

“36% of the 250 surveyed students chose fall” is a complete summary: statistic, group, and size.

3. Worked examples

Write the formula, plug in, then answer in context.

Question	Formula	Work	Answer
48 of 120 students ride the bus. Relative frequency?	count ÷ total	48 ÷ 120	0.40 (40% of the students)
35% of 600 shoppers paid with cash. How many?	proportion × total	0.35 × 600	210 shoppers
72 people, which is 18% of the sample, chose Rock. Sample size?	count ÷ proportion	72 ÷ 0.18	400 people
Relative frequencies 0.5, 0.2, 0.2, and ?	1 − sum of the others	1 − 0.9	0.1

4. On the FRQ

How to earn the points

Show the division: “48/120 = 0.40.” A bare number can lose the communication point.
Interpret in context with the denominator: “40% of the 120 students surveyed ride the bus.”
When comparing groups of different sizes, compare proportions, not counts, and say so.
Name the mode as a category (“Bus”), not as a number.

Common mistakes

Dividing the total by the count instead of the count by the total.
Comparing raw counts between groups of different sizes.
Reporting a mean or median for a categorical variable.
Forgetting that relative frequencies must add to 1, which is a quick way to find a missing value.

5. Practice questions

AP-style multiple choice. Pick an answer to see the explanation.

0 / 0 correct

6. Key terms

The vocabulary for topic 1.3. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 1 terminology guide.