Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Relative Frequency.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in Statistics.
Concept Recap
Relative frequency is the fraction or percentage of times a value occurs out of the total number of observations. It converts raw counts into proportions, enabling fair comparisons between groups of different sizes.
Instead of saying '15 students picked pizza,' you say '15 out of 50' or '30%.' Relative frequency compares to the whole, making different-sized groups comparable.
Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:Relative Frequency asks whether the same cases connect two variables or groups in a pattern that can be described carefully.
Common stuck point:Students often know a procedure related to relative frequency but skip the recognition step: Am I studying a relationship between variables, and have I separated association from causation? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Am I studying a relationship between variables, and have I separated association from causation?
Worked Examples
Example 1
medium
A survey of 200 people lists ice-cream flavors: vanilla 80, chocolate 60, strawberry 40, other 20. Build the relative frequency table.Survey of 200 people: ice-cream flavor frequencies and relative frequencies.
Two coins were flipped together 80 times. HH: 22, HT: 18, TH: 20, TT: 20. Build the relative frequency table and identify the most common outcome.80 two-coin flips: HH=22, HT=18, TH=20, TT=20. Build the relative frequency table and find the most common outcome.
Example 3
easy
In a class of 30 students, 12 walk to school, 10 take the bus, 5 cycle, and 3 are driven. Calculate the relative frequency of each transport method.
Example 4
medium
A die is rolled 200 times with results: 1→30, 2→38, 3→35, 4→32, 5→28, 6→37. Calculate the relative frequency for each outcome and discuss whether the die appears fair.
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
In a class of 25 students, 10 chose soccer. What is the relative frequency of soccer (as a fraction)?
Example 2
easy
Out of 50 spins, a spinner landed on red 20 times. Express the relative frequency of red as a percent.
Example 3
easy
A bag has 40 marbles; 8 are blue. What is the relative frequency of blue marbles?
Example 4
easy
In 200 emails, 30 were spam. What fraction were spam?
Example 5
easy
A survey of 60 people found 45 own a phone. What is the relative frequency of phone owners?
Example 6
easy
If a category's relative frequency is 0.25 and there are 80 observations total, how many are in that category?
Example 7
easy
Three categories have counts 12, 18, and 30. What is the relative frequency of the third category?Three categories with counts 12, 18, and 30. Find the relative frequency of the third category.
Example 8
easy
A relative frequency is reported as 207. Convert it to a percent.
Example 9
medium
Class A: 12 of 30 passed. Class B: 18 of 40 passed. Which class had the higher pass relative frequency?
Example 10
medium
A store sold 150 items: 60 small, 50 medium, 40 large. What percent were medium (round to nearest whole percent)?A store sold 150 items. What percent were Medium?
Example 11
medium
Two surveys: Survey 1 found 40 of 200 dissatisfied; Survey 2 found 30 of 120 dissatisfied. Which has the higher dissatisfaction rate?
Example 12
medium
A category has relative frequency 0.18. If that category contains 27 observations, what is the total number of observations?
Example 13
medium
In 250 trials a result occurred with relative frequency 0.36. How many times did it occur?
Example 14
medium
A pie of responses: Yes =0.5, No =0.3, the rest Maybe. If there are 200 responses, how many said Maybe?
Example 15
medium
Group X: relative frequency of success 0.6 over 50 trials. Group Y: 0.4 over 100 trials. What is the combined success relative frequency?
Example 16
medium
A relative frequency table must have entries summing to 1. Three entries are 0.22, 0.31, and 0.19. What must the fourth be?Four relative frequencies summing to 1: 0.22, 0.31, 0.19, and one unknown. Find the fourth entry.
Example 17
medium
A spinner landed on blue with relative frequency 0.28 over 75 spins. How many blue results?
Example 18
challenge
Two classes are combined. Class P: pass rate 0.8 with n students. Class Q: pass rate 0.5 with 40 students. The combined pass rate is 0.65. Find n.
Example 19
challenge
A four-category relative frequency distribution is in arithmetic progression with common difference 0.1 and the smallest entry p. Find p and the largest entry.
Example 20
challenge
A category's count must be a whole number. The total is 73 and a category's relative frequency is reported as 0.30. Show why the reported relative frequency cannot be exact, and give the nearest exact relative frequency below it.
Example 21
easy
A coin is flipped 100 times and lands heads 53 times. What is the relative frequency of heads as a decimal?
Example 22
easy
A class has 32 students; 24 own a bicycle. What is the relative frequency of bicycle owners?
Example 23
easy
In a sample of 40 dice rolls, the number 6 appeared 8 times. What is the relative frequency of rolling a 6?
Example 24
easy
Of 250 customers, 40 returned an item. Express the return rate as a percent.
Example 25
easy
A relative frequency table shows soccer =0.4, basketball =0.25, tennis =0.15. What is the relative frequency for the remaining category?
Example 26
easy
In a survey of 20 people, 5 said they exercise daily. What is the relative frequency of daily exercisers?
Example 27
medium
A survey records 80 people. Relative frequency of vegetarians is 81. How many vegetarians are in the survey?
Example 28
medium
In Town A, 30 of 120 households recycle. In Town B, 45 of 150 households recycle. Which town has a higher recycling rate?
Example 29
medium
A spinner with sectors red, blue, green is spun 500 times: red =200, blue =175. Estimate the probability of green from these data.
Example 30
medium
A category's relative frequency is 32 in a sample of 300. How many observations are in that category?
Example 31
medium
From a frequency table: A =18, B =27, C =15. What is the relative frequency of category B as a decimal (round to two places)?
Example 32
medium
A class of 40 students had test results: A: 10, B: 16, C: 10, F: 4. What percent earned a B?
Example 33
medium
A spinner is spun 200 times: red lands 80, blue 70, green 50. If the next 300 spins give similar relative frequencies, how many would we predict to be blue?
Example 34
medium
Two classes report quiz results: Class X 12 of 30 got an A; Class Y 21 of 60 got an A. Which class has the higher A-rate?
Example 35
hard
In a survey, 60% of 200 respondents are female. Of females, 70% own a pet. What is the relative frequency of female pet-owners in the survey?
Example 36
hard
As a die is rolled more times, the relative frequency of each face is expected to approach what value (for a fair die)?
Example 37
hard
In a class of 25 students, the relative frequency of left-handed students is 0.12. How many left-handed students are there, and is this a whole number?
Example 38
hard
A category's relative frequency is reported as 0.27 in a sample. The sample size is 40. Could this be exact?
Example 39
hard
A grade distribution: A 0.10, B 0.30, C 0.40, D 0.15, F unknown. What is F's relative frequency, and in a class of 60 how many F's?Grade distribution: A=0.10, B=0.30, C=0.40, D=0.15, F=? Find F's relative frequency.
Example 40
challenge
A spinner gives outcomes A, B, C, D with relative frequencies in the ratio 2:3:4:1 after 100 spins. How many times did C occur?
Example 41
medium
School A has 400 students (60 in sports clubs) and School B has 250 students (45 in sports clubs). Which school has a higher proportion of students in sports clubs?
Example 42
hard
A coin is flipped repeatedly. After 10 flips: 7 heads (RF=0.70). After 50 flips: 29 heads (RF=0.58). After 500 flips: 256 heads (RF=0.512). After 5000 flips: 2,520 heads (RF=0.504). Describe the trend and explain what it demonstrates about probability.