Relative frequency describes how often an outcome occurs compared with the total number of observations. It turns raw counts into proportions, decimals, or percentages so different data sets can be compared fairly. This matters because a count of 12 can mean something very different in a sample of 20 than in a sample of 200.
Relative frequency is a bridge between collected data and probability thinking.
Key Facts
- Relative frequency = frequency of an outcome / total number of observations
- As a decimal: relative frequency = f / n
- As a percentage: relative frequency percent = (f / n) × 100%
- The sum of all relative frequencies in a complete data table is 1, or 100%
- Experimental probability uses data: P(outcome) ≈ relative frequency of that outcome
- Larger sample sizes usually give more stable relative frequencies than smaller samples
Vocabulary
- Frequency
- The number of times a particular outcome or category appears in a data set.
- Relative Frequency
- The fraction or proportion of the total data represented by one outcome or category.
- Proportion
- A comparison of one part to the whole, often written as a fraction or decimal.
- Percentage
- A proportion expressed out of 100.
- Experimental Probability
- A probability estimate based on observed results from trials or collected data.
Common Mistakes to Avoid
- Dividing by the wrong total, such as using the number in another category instead of the full sample size. Relative frequency must compare the category count to the total number of observations.
- Forgetting to convert a decimal to a percent correctly. For example, 0.35 equals 35%, not 0.35%.
- Adding counts and relative frequencies in the same column as if they have the same unit. Counts are raw numbers, while relative frequencies are proportions of the whole.
- Treating experimental probability as guaranteed future results. Relative frequency estimates probability from data, but random variation can still cause different results in future trials.
Practice Questions
- 1 A survey of 80 students found that 28 chose soccer as their favorite sport. Find the relative frequency as a fraction, decimal, and percentage.
- 2 A spinner is spun 50 times and lands on blue 14 times, red 21 times, and green 15 times. Find the relative frequency for each color and check that the percentages add to 100%.
- 3 Two classes both report that 10 students prefer online homework. Class A has 20 students and Class B has 40 students. Explain which class has the greater relative frequency and why counts alone can be misleading.