Difference Between Frequency and Relative Frequency

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%

Do Check,

• Mean
• Mean, Median and Mode

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%

FAQs

Question 1: What is the difference between frequency and relative frequency?

Answer:

Frequency counts the number of times a value or category appears in a dataset, while relative frequency calculates the proportion or percentage of the dataset that value or category represents.

Question 2: How do you calculate frequency?

Answer:

The formula to calculate the frequency is,

Frequency = Number of Times Value (Category) Appears in Dataset

Question 3: How do you calculate relative frequency?

Answer:

The formula to calculate the relative frequency is,

Relative Frequency = Frequency / Total Number of Data Points in Dataset

Question 4: What is the range of values for frequency?

Answer:

Frequency can be any whole number between 0 and the total number of data points in the dataset.

Question 5: What is the range of values for relative frequency?

Answer:

Relative frequency can be any decimal number between 0 and 1 or expressed as a percentage between 0% and 100%.

Question 6: Why is frequency important in statistics?

Answer:

Frequency is important in statistics because it provides information on how often specific values or categories appear in a dataset, which can help to identify patterns and trends in the data.