Frequency and relative frequency are two fundamental concepts in statistics. They describe how often values or categories appear in a dataset, and what proportion of the dataset they represent.
In this article, we will discuss the difference between frequency and relative frequency, and how to calculate them.
Frequency
Frequency is the number of times a specific value or category appears in a dataset. The formula for frequency is given below in the diagram.
For example, consider the following dataset, 1, 2, 3, 2, 1, 2, 4, 1, 2, 3. To calculate the frequency of the value 2, we count the number of times it appears in the dataset, which is 4.
Steps to Calculate Frequency
Use the step given below to calculate the frequency.
- Identify the value or category you want to calculate the frequency for.
- Count the number of times the value/category appears in the dataset.
- The result is the frequency of that value/category in the dataset.
Relative Frequency
Relative frequency is the proportion or percentage of times a specific value or category appears in a dataset. The formula for relative frequency is given below in the diagram
For example, using the same dataset as before, to calculate the relative frequency of the value 2, we first calculate its frequency (which is 4). The total number of data points in the dataset is 10. Therefore, the relative frequency of the value 2 is:
Relative Frequency of 2 = 4 / 10 = 0.4 or 40%
Steps to Calculate Relative Frequency
Use the step given below to calculate the relative frequency.
- Identify the value or category you want to calculate the relative frequency for.
- Calculate the frequency of that value/category using the formula mentioned earlier.
- Calculate the total number of data points in the dataset.
- Divide the frequency by the total number of data points.
- The result is the relative frequency of that value/category in the dataset.
Learn More about Relative Frequency
Difference Between Frequency and Relative Frequency
The main differences between frequency and relative frequency are,
| Frequency | Relative Frequency |
|---|---|
| Frequency counts the number of times a value or category appears in the dataset | Relative frequency calculates the proportion or percentage of the dataset that value or category represents. |
| Frequency uses whole numbers | Relative frequency uses decimal numbers or percentages |
| Frequency cannot be greater than the total number of data points in the dataset | Relative frequency can be any value between 0 and 1 or expressed as a percentage between 0% and 100% |
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Solved Examples
Example 1: In a survey of 50 people, the following data were collected on the number of hours they spend on social media per day,
| Hours | Frequency |
|---|---|
| 0-1 | 10 |
| 1-2 | 15 |
| 2-3 | 12 |
| 3-4 | 8 |
| 4-5 | 5 |
Calculate the relative frequency of each category.
Solution:
The total number of people surveyed is 50.
Hours Frequency Relative Frequency 0-1 10 10 / 50 = 0.20 1-2 15 15 / 50 = 0.30 2-3 12 12 / 50 = 0.24 3-4 8 8 / 50 = 0.16 4-5 5 5 / 50 = 0.10 To calculate the relative frequency of each category, we divide the frequency of each category by the total number of people surveyed.
Example 2: A survey was conducted on the number of cars owned by households in a particular area. The following data was obtained.
| Cars | Frequency |
|---|---|
| 0 | 25 |
| 1 | 50 |
| 2 | 30 |
| 3 | 10 |
| 4 | 5 |
Calculate the total number of households surveyed.
Solution:
Total Number of households surveyed is the sum of all the frequencies.
Total number of Households = 25 + 50 + 30 + 10 + 5 = 120
Example 3: In a class of 40 students, the following marks were obtained in a test,
| Marks | Frequency |
|---|---|
| 0-10 | 8 |
| 10-20 | 12 |
| 20-30 | 15 |
| 30-40 | 5 |
What is the percentage of students who scored less than 20 marks?
Solution:
Total number of students is 40.
The frequency of students who scored less than 20 marks is the sum of the frequency of marks ranging from 0-10 and 10-20, which is 8 + 12 = 20.
Percentage of students who scored less than 20 marks = (20/40) × 100%
= 50%
Example 4: In a survey, 60 people were asked about their favourite ice cream flavour. The results were as follows,
| Flavour | Frequency |
|---|---|
| Vanilla | 30 |
| Chocolate | 20 |
| Strawberry | 5 |
| Butter Pecan | 5 |
What is the relative frequency of Vanilla flavour?
Solution:
The total number of responses is 60
The frequency of the Vanilla flavour is 30
The relative frequency of Vanilla flavour is calculated by dividing its frequency by the total number of responses.
Relative frequency of Vanilla flavour = 30/60 = 0.5 or 50%.
Example 5: In a store, 50 customers were surveyed on the amount of money they spent on groceries. The following data was obtained,
| Amount | Frequency |
| 0-100 | 10 |
| 100-200 | 20 |
| 200-300 | 15 |
| 300-400 | 4 |
| 400-500 | 1 |
What is the total amount spent on groceries by the customers surveyed?
Solution:
We can calculate the total amount spent on groceries by multiplying each category by its frequency and adding the results.
Total amount spent on groceries = (10 × 50) + (20 × 150) + (15 × 250) + (4 × 350) + (1 × 450)
= 1000 + 3000 + 3750 + 1400 + 450
= 9600
Example 6: In a class of 30 students, the following marks were obtained in a test,
| Marks | Frequency |
|---|---|
| 0-10 | 6 |
| 10-20 | 12 |
| 20-30 | 8 |
| 30-40 | 4 |
What is the percentage of students who scored between 10 and 30 marks?
Solution:
Total number of students is 30.
The frequency of students who scored between 10 and 30 marks is the sum of the frequency of marks ranging from 10-20 and 20-30, which is 12 + 8 = 20.
Percentage of students who scored between 10 and 30 marks = (20/30) x 100% = 66.67%