In statistics and data analysis, understanding how often events occur within a dataset is useful for drawing conclusions and making predictions.
Two important concepts that help quantify occurrences are frequency and relative frequency. While both deal with counting how often something happens, they are used in slightly different contexts.
In this article, we’ll explain the difference between frequency and relative frequency, how they are calculated, and provide examples to show how each is used in practice.
What Is Frequency?
Frequency refers to the number of times an event or value occurs in a dataset. It is simply the count of how often something happens. Frequency gives you a basic understanding of the distribution of data by telling you how often a specific category or value appears.
For example, in a survey where you ask 50 people about their favorite color, if 20 people say blue, then the frequency of people who like blue is 20.
Formula for Frequency
Frequency = Number of occurrences of a specific event or value
Frequency is typically represented in tables or graphs, such as frequency distributions or histograms, where each bar represents the count of occurrences of a specific value.
What Is Relative Frequency?
Relative frequency goes a step further than frequency by showing the proportion or percentage of times an event occurs in relation to the total number of events. Rather than just counting how many times something happens, relative frequency tells you how significant that occurrence is relative to the entire dataset. It gives a more comparative view of data.
Relative frequency is useful when you want to compare how often different events happen, especially when working with datasets of different sizes.
Formula for Relative Frequency
Relative Frequency = (Frequency of a specific event/Total number of events) × 100
Relative frequency is often expressed as a percentage or a decimal, which makes it easier to compare different categories or events.
Example: Frequency vs Relative Frequency
Let’s consider an example where you ask 30 people their favorite fruit. The results are:
- 10 people say Apple
- 8 people say Banana
- 5 people say Orange
- 7 people say Grape
Frequency Table
| Fruit | Frequency |
|---|---|
| Apple | 10 |
| Banana | 8 |
| Orange | 5 |
| Grape | 7 |
In this table, the frequency simply shows the count of how many people chose each fruit.
Relative Frequency Table
To calculate the relative frequency, you divide each fruit’s frequency by the total number of responses (30) and then multiply by 100 to convert it to a percentage.
Relative Frequency = Frequency/Total Responses × 100
| Fruit | Relative Frequency |
|---|---|
| Apple | 10/30 × 100 = 33.33 % |
| Banana | 8/30 × 100 = 26.67 % |
| Orange | 5/30 × 100 = 16.67 % |
| Grape | 7/30 × 100 = 23.33 % |
In this table, the relative frequency shows the proportion of people who chose each fruit as a percentage of the total responses.
Key Differences Between Frequency and Relative Frequency
| Aspect | Frequency | Relative Frequency |
|---|---|---|
| Definition | The number of times an event occurs | The proportion or percentage of times an event occurs relative to the total |
| Formula | Count of occurrences | Frequency/Total Responses × 100 |
| Example | 10 people chose Apple | 33.33% of people chose Apple |
| Purpose | Shows absolute counts of events | Shows the relative significance of events in comparison to the whole dataset |
| Expressed as | Whole numbers or counts | Decimals, fractions, or percentages |
When to Use Frequency and Relative Frequency
Both frequency and relative frequency are useful, but they serve slightly different purposes depending on the context.
Use Frequency when:
- You are working with small datasets and only need the basic counts of how often something happens.
- You want to create frequency distributions or histograms to visually represent how often different values occur in a dataset.
- You’re only concerned with specific counts, like the number of people who fall into different categories (e.g., how many people in a survey picked a particular answer).
Use Relative Frequency when:
- You need to understand the proportion or percentage of events in comparison to the total.
- You are comparing the occurrence of events in datasets of different sizes. For example, if two different surveys have different numbers of respondents, relative frequency helps compare their results fairly.
- You want to create a relative frequency distribution to understand the overall pattern of the data and the significance of each event.
For example, if you conduct two surveys with different sample sizes (one with 100 people and one with 50 people), relative frequency will give you a fair comparison between the two surveys, while frequency alone might be misleading due to the different sample sizes.
Real-World Applications of Frequency and Relative Frequency
1. Market Research
In market research, companies often use frequency to see how many times customers prefer one product over another. Relative frequency, on the other hand, shows the percentage of customers who prefer a product, giving a clearer picture of consumer preferences.
2. Sports Statistics
In sports, frequency might be used to count how many times a player scores in a season, while relative frequency can show the percentage of times the player scores compared to all the games they play.
3. Quality Control
Manufacturers may use frequency to count the number of defective products in a batch, and relative frequency to show the percentage of defects relative to the total production output.
Summary
In summary, frequency and relative frequency are both important tools in data analysis:
- Frequency gives you the raw count of how often something happens.
- Relative frequency provides a proportion or percentage that shows how significant that count is compared to the whole dataset.