Relative frequency is found by dividing the frequency of a category by the total number of observations, often writing the result as a decimal, fraction, or percentage.

What is relative frequency?

Relative frequency tells you how often something happens compared to the total number of cases. It is commonly used in statistics to estimate probabilities from data.

In simple terms:
“Relative frequency = part ÷ whole.”

Formula for relative frequency

The standard formula is:

Relative frequency=frequency of category (f)total number of observations (n)\text{Relative frequency}=\frac{\text{frequency of category }(f)}{\text{total number of observations }(n)}Relative frequency=total number of observations (n)frequency of category (f)​

Key pieces you need:

  • f : how many times that category/event occurs.
  • n : total number of data points.

You can then express the result as:

  • A decimal (e.g., 0.25).
  • A fraction (e.g., 5/20).
  • A percentage : relative frequency × 100% (e.g., 25%).

Step‑by‑step: how to find relative frequency

  1. Collect the data.
    • Example: You roll a die 30 times and get the number 6 exactly 5 times.
  1. Count the frequency for each category.
    • Category = “rolled a 6” → frequency f=5f=5f=5.
 * Total rolls n=30n=30n=30.
  1. Apply the formula f/nf/nf/n.
    • Relative frequency of rolling a 6 = 5/305/305/30.
 * As a decimal: 5/30≈0.1675/30\approx 0.1675/30≈0.167.

 * As a percent: 0.167×100%≈16.7%0.167\times 100\%\approx 16.7\%0.167×100%≈16.7%.
  1. Repeat for all categories if you have more than one (e.g., each face of a die, each answer choice in a survey).
  1. Check the sum.
    • If you express all relative frequencies as decimals, they should add up to about 1 (small rounding errors are normal).
 * As percentages, they should sum to about 100%.

Example with a small table

Suppose 20 students are asked their favorite fruit and the responses are:

  • Apple: 8
  • Banana: 6
  • Orange: 4
  • Grape: 2

Total students n=20n=20n=20.

Here is how relative frequency looks in a table (as HTML, per your rules):

html

<table>
  <thead>
    <tr>
      <th>Fruit</th>
      <th>Frequency (f)</th>
      <th>Relative Frequency (f / 20)</th>
      <th>Relative Frequency (%)</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>Apple</td>
      <td>8</td>
      <td>8 / 20 = 0.40</td>
      <td>40%</td>
    </tr>
    <tr>
      <td>Banana</td>
      <td>6</td>
      <td>6 / 20 = 0.30</td>
      <td>30%</td>
    </tr>
    <tr>
      <td>Orange</td>
      <td>4</td>
      <td>4 / 20 = 0.20</td>
      <td>20%</td>
    </tr>
    <tr>
      <td>Grape</td>
      <td>2</td>
      <td>2 / 20 = 0.10</td>
      <td>10%</td>
    </tr>
    <tr>
      <td><strong>Total</strong></td>
      <td>20</td>
      <td>0.40 + 0.30 + 0.20 + 0.10 = 1.00</td>
      <td>40% + 30% + 20% + 10% = 100%</td>
    </tr>
  </tbody>
</table>

Each relative frequency is just frequency ÷ 20, which is the total number of students.

Relative vs cumulative relative frequency

  • Relative frequency: single category’s proportion (for one row of the table).
  • Cumulative relative frequency: running total of the relative frequencies up to that row.

Example: suppose weekly sales have relative frequencies 0.19, 0.33, 0.27, 0.21:

  • Week 1 cumulative: 0.19
  • Week 2 cumulative: 0.19 + 0.33 = 0.52
  • Week 3 cumulative: 0.52 + 0.27 = 0.79
  • Week 4 cumulative: 0.79 + 0.21 = 1.00

The last cumulative relative frequency should be 1 (or 100%), meaning it covers all the data.

Quick memory trick

Think:

“Relative frequency = count in group / total count.”

If you can identify the group’s count and the total, you can always find the relative frequency by dividing and, if you like, converting to a percentage.

TL;DR:
To find relative frequency, take the frequency of a category, divide it by the total number of observations, and optionally convert to a percent; all relative frequencies together should sum to about 1 (or 100%).