AP® Statistics · Unit 1 · Topic 1.3
Frequency and Relative Frequency Tables
A frequency table shows how many observations fall into each category; a relative frequency table shows what share of the total each category makes up, found by dividing each count by the total.
A frequency table just lists each category next to its raw count: how many people, objects, or outcomes landed there. That's useful, but raw counts only mean something next to a total. If a class of 20 has 15 students who like pizza, that's a huge majority. If a school of 2000 has 15 students who like pizza, that's almost nobody. Same count, totally different story. Relative frequency fixes this by dividing each category's count by the total number of observations, turning counts into proportions (or percentages) that you can compare fairly across groups of different sizes.
To build one: get your raw counts for every category, add them up to find the total, then divide each category's count by that total. Check that your relative frequencies add up to 1 (or 100%) — that's your proof you didn't drop or double-count anyone. For 240 survey answers split across categories, each category's relative frequency is simply its count divided by 240, and all of those fractions together should sum to 1.
Relative frequency tables set up everything that follows in this unit: bar graphs and pie charts are just pictures of these proportions, and comparing distributions across groups (like comparing two surveys) only works cleanly when you've converted to relative frequencies first. Keep the distinction straight: frequency answers 'how many,' relative frequency answers 'what fraction of the whole.'
Key terms
- Frequency
- The raw count of observations that fall into a category.
- Relative frequency
- A category's count divided by the total number of observations, expressed as a fraction, decimal, or percent.
- Categorical data
- Data that sorts observations into named groups rather than numerical measurements.
- Distribution
- The pattern of how often each category or value occurs across all observations.
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End of topic.