📊 How to Construct a Relative Frequency Table (Simple Step-by-Step Guide)
A relative frequency table is used in statistics to show how often something happens, but in terms of a fraction or percentage of the total.
Instead of only counting how many times a value appears, it answers:
✅ “Out of the total, what part does this item represent?”
This makes data easier to compare, especially when sample sizes are different.
What is Relative Frequency?
Relative Frequency = Frequency ÷ Total Number of Observations
Example:
If 10 students like apples out of 40,
Relative frequency = 10 / 40 = 0.25 (or 25%)
Step-by-Step: How to Construct a Relative Frequency Table
✅ Step 1 — Collect Your Data
Suppose we asked 20 students which fruit they like:
| Fruit | Students (Frequency) |
|---|---|
| Apple | 6 |
| Banana | 4 |
| Mango | 5 |
| Orange | 5 |
✅ Total students = 6 + 4 + 5 + 5 = 20
✅ Step 2 — Add a Column for Relative Frequency
Formula:
Relative Frequency = Frequency ÷ Total
Now fill the table:
| Fruit | Frequency | Relative Frequency |
|---|---|---|
| Apple | 6 | 6/20 = 0.30 |
| Banana | 4 | 4/20 = 0.20 |
| Mango | 5 | 5/20 = 0.25 |
| Orange | 5 | 5/20 = 0.25 |
✅ Check sum of relative frequencies:
0.30 + 0.20 + 0.25 + 0.25 = 1.00
(Always equals 1 or 100%)
✅ Step 3 — Convert to Percentage (Optional)
Multiply by 100.
| Fruit | Frequency | Relative Frequency | Percentage |
|---|---|---|---|
| Apple | 6 | 0.30 | 30% |
| Banana | 4 | 0.20 | 20% |
| Mango | 5 | 0.25 | 25% |
| Orange | 5 | 0.25 | 25% |
✅ Now it clearly shows which fruit is most and least popular.
Example 2 — Constructing a Relative Frequency Table for Dice Rolls
Suppose a dice was rolled 10 times, results:
2, 3, 5, 3, 6, 2, 1, 3, 5, 2
Step 1: Count frequencies
| Number | Frequency |
|---|---|
| 1 | 1 |
| 2 | 3 |
| 3 | 3 |
| 4 | 0 |
| 5 | 2 |
| 6 | 1 |
Step 2: Divide by total rolls (10)
| Number | Frequency | Relative Frequency |
|---|---|---|
| 1 | 1 | 1/10 = 0.10 |
| 2 | 3 | 3/10 = 0.30 |
| 3 | 3 | 3/10 = 0.30 |
| 4 | 0 | 0/10 = 0.00 |
| 5 | 2 | 2/10 = 0.20 |
| 6 | 1 | 1/10 = 0.10 |
Why Do We Use Relative Frequency Tables?
| Benefit | Explanation |
|---|---|
| Easy Comparison | Even if sample sizes change |
| Shows Patterns | Which value is most common |
| Helps in Probability | Useful in statistics & data science |
| Works for Surveys, Experiments, Games | Very flexible |
Common Mistakes & Fixes
❌ Forgetting total number
✅ Always add all frequencies first
❌ Relative frequencies don’t add up to 1
✅ Check rounding — use 2–4 decimal places
❌ Mixing frequency and relative frequency
✅ Frequency = count, Relative = fraction/decimal/percentage
Visualizing Relative Frequency
You can convert the table into:
- Pie Chart
- Bar Graph
- Histogram
Helpful Links
- Khan Academy Statistics: https://www.khanacademy.org/math/statistics-probability
- Statistics How-To: https://www.statisticshowto.com
FAQs
✅ 1. What is a relative frequency table in statistics?
It is a table that shows how often each value occurs compared to the total. It uses fractions, decimals, or percentages to make data easier to compare.
✅ 2. How do you calculate relative frequency?
Use this formula:
Relative Frequency = Frequency ÷ Total Observations
Example: 4 out of 20 = 4/20 = 0.20 or 20%
✅ 3. Do relative frequencies add up to 1?
Yes. If you add all relative frequencies, the total equals 1 (or 100%).
✅ 4. What is the difference between frequency and relative frequency?
- Frequency = number of times a value appears
- Relative frequency = frequency ÷ total, showing proportion
✅ 5. Where are relative frequency tables used?
- Surveys
- Experiments
- Games like dice or cards
- Business reports
- School statistics
- Data analysis and probability
✅ Final Summary
Constructing a relative frequency table is simple:
1️⃣ Gather data
2️⃣ Count frequencies
3️⃣ Divide each value by the total
4️⃣ (Optional) Convert to percentage
Relative frequency tables help compare data more clearly and are important in statistics, probability, and data science.