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URL: https://nakafa.com/en/subjects/mathematics/statistics-foundations/relative-frequency
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Calculate relative frequency to find data proportions and percentages. Learn to compare groups and interpret statistical results with clear examples.

---

## Understanding Relative Frequency

You surely know what frequency is, right? Frequency is simply **how many times** a value or data point appears in a dataset.

For example, if we ask $$30 \text{ students}$$ about their phone brands, and $$10 \text{ students}$$ answer "Apple", then the frequency for the "Apple" brand is $$10$$.

Visible text: For example, if we ask about their phone brands, and answer "Apple", then the frequency for the "Apple" brand is .

Now, we will get acquainted with **Relative Frequency**. What is it?

Relative Frequency is how we look at the frequency of a data point **compared to the total number of all data points**. So, it's not just about how many times it appears, but we look at the "part" or "proportion" of that data relative to the whole.

### Why Do We Need Relative Frequency?

Relative frequency is very important, you know. With relative frequency, we can:

1. **Compare Proportions**: We can compare how large the proportion of one data group is compared to another group within the same dataset. For example, how large the proportion of Apple users is compared to Samsung users in one respondent group.
2. **Compare Between Different Groups**: We can compare the proportion of data from two groups with different total numbers. For example, comparing the percentage of students who like math in group A (total $$30 \text{ students}$$) with group B (total $$40 \text{ students}$$). It would be difficult with just regular frequency, but with relative frequency (percentage), the comparison becomes fair.

Visible text: 1. **Compare Proportions**: We can compare how large the proportion of one data group is compared to another group within the same dataset. For example, how large the proportion of Apple users is compared to Samsung users in one respondent group.
2. **Compare Between Different Groups**: We can compare the proportion of data from two groups with different total numbers. For example, comparing the percentage of students who like math in group A (total ) with group B (total ). It would be difficult with just regular frequency, but with relative frequency (percentage), the comparison becomes fair.

## Relative Frequency Formula

Calculating it is super easy!

```math
\text{Relative Frequency} = \frac{\text{Group Frequency}}{\text{Total Frequency}}
```

Where:

- **Group Frequency**: This is how many times the data or value in that group appears.
- **Total Frequency**: This is the total number of all data points we observed.

Relative Frequency is usually expressed in the form of:

- **Fraction**: The most basic form of division.
- **Decimal**: The result of the fraction division.
- **Percentage**: The decimal form multiplied by $$100\%$$. This is the most commonly used because it's easy to understand.

Visible text: - **Fraction**: The most basic form of division.
- **Decimal**: The result of the fraction division.
- **Percentage**: The decimal form multiplied by . This is the most commonly used because it's easy to understand.

## Example of Calculating Relative Frequency

Let's use the phone brand data example from the $$30 \text{ students}$$ earlier:

Visible text: Let's use the phone brand data example from the earlier:

| Phone Brand | Frequency (Number of Students) |
| :---------- | :----------------------------- |
| Apple       | $$12$$       |
| Samsung     | $$10$$       |
| Xiaomi      | $$8$$        |
| **Total**   | $$30$$       |

Visible text: | Phone Brand | Frequency (Number of Students) |
| :---------- | :----------------------------- |
| Apple | |
| Samsung | |
| Xiaomi | |
| **Total** | |

Total frequency is $$12 + 10 + 8 = 30$$ students.

Visible text: Total frequency is students.

Now let's calculate the relative frequency for each brand:

1. **Apple**:

   
   
   ```math
   \text{Relative Frequency Apple} = \frac{12}{30}
   ```

   Relative Frequency Apple is $$0.4$$

   In percent: $$0.4 \times 100\% = 40\%$$

2. **Samsung**:

   
   
   ```math
   \text{Relative Frequency Samsung} = \frac{10}{30}
   ```

   Relative Frequency Samsung is $$0.333...$$ (we round it to $$0.33$$)

   In percent: $$0.33 \times 100\% = 33\%$$

3. **Xiaomi**:

   
   
   ```math
   \text{Relative Frequency Xiaomi} = \frac{8}{30}
   ```

   Relative Frequency Xiaomi is $$0.266...$$ (we round it to $$0.27$$)

   In percent: $$0.27 \times 100\% = 27\%$$

Visible text: 1. **Apple**:

 
 

 Relative Frequency Apple is 

 In percent: 

2. **Samsung**:

 
 

 Relative Frequency Samsung is (we round it to )

 In percent: 

3. **Xiaomi**:

 
 

 Relative Frequency Xiaomi is (we round it to )

 In percent:

**Relative Frequency Table:**

| Phone Brand | Frequency                | Relative Frequency (Decimal) | Relative Frequency (Percent) |
| :---------- | :----------------------- | :--------------------------- | :--------------------------- |
| Apple       | $$12$$ | $$0.40$$   | $$40\%$$   |
| Samsung     | $$10$$ | $$0.33$$   | $$33\%$$   |
| Xiaomi      | $$8$$  | $$0.27$$   | $$27\%$$   |
| **Total**   | $$30$$ | $$1.00$$   | $$100\%$$  |

Visible text: | Phone Brand | Frequency | Relative Frequency (Decimal) | Relative Frequency (Percent) |
| :---------- | :----------------------- | :--------------------------- | :--------------------------- |
| Apple | | | |
| Samsung | | | |
| Xiaomi | | | |
| **Total** | | | |

The sum of relative frequencies (in decimal form) should always be $$1$$, and in percent should be $$100\%$$. There might be slight differences due to rounding, but it should be very close to $$1$$ or $$100\%$$.

Visible text: The sum of relative frequencies (in decimal form) should always be , and in percent should be . There might be slight differences due to rounding, but it should be very close to or .

## Interpreting Relative Frequency

From the relative frequency table above, we can say:

- $$40\%$$ of the students in that group use Apple brand phones.
- About $$33\%$$ students use Samsung.
- The rest, about $$27\%$$, use Xiaomi.

Visible text: - of the students in that group use Apple brand phones.
- About students use Samsung.
- The rest, about , use Xiaomi.

With relative frequency, we get a clearer picture of the proportion of each phone brand among the $$30 \text{ students}$$.

Visible text: With relative frequency, we get a clearer picture of the proportion of each phone brand among the .

So, relative frequency helps us understand how large the "portion" of a data point is within the entire dataset. Easy, right?