How to find the Relative Frequency?
The term ‘relative’ is used to denote that an act is being observed in comparison to something other. Frequency is a way to calculate how repeatedly a particular action takes place. Relative frequency is a way to find how regularly a particular action takes place against total events. To calculate relative frequency two things are important
1. Number of total events/occurrences
2. Frequency count for a subgroup/category
Relative frequency: Subgroup frequency/ total frequency
Relative frequency: f/n
Here,
f = Number of times an event occurred in an observation
n = frequency
How to Calculate Relative Frequency?
Frequencies can be converted into relative frequencies by following these steps
Step 1: Find the frequency in the given data
Step 2: Then the frequency should be divided by N (total number).
Suppose for example Gopal surveys a group of students in his college to find their favorite game. The data processed by him is represented in graphical form below. What will be the relative frequency of students whose favorite game is cricket?
The total number of students in the above-given data set is found by the addition of the heights of the bars
5+10+25+15 = 55
from the above graphical representation The number of students whose favorite game is cricket are 5
So, the relative frequency for the cricket will be = f/N = 5/55= 0.09 = 9%
Cumulative relative frequency
The addition of all of the previous relative frequencies to the relative frequency for the current row is called cumulative relative frequency
Sample Problems
Problem 1: A die is tossed 50 times and it falls 5 times on the number 6. Then find the relative frequency?
Solution:
Given, Number of times a die is tossed = 50
Number of times it falls on number 6 = 5
From the formula,
Relative frequency = Number of positive occurrences/Total Number of occurrences
f = 5/50 = 0.1
Therefore, the relative frequency of the die that fell on the number 6 is 0.1
Problem 2: A coin is tossed 90 times, and the coin falls on heads 24 times. What is the relative frequency of the coin falling on tails?
Solution:
Relative frequency = number of times an act has occurred / number of occurrences
The act taken into consideration is the coin falling on tails = 90 – 24 = 66 times
Relative frequency of the coin falling on tails = 66/90 = 0.733 = 73.3%
Problem 3: If 10 students travel to school by car, another 10 students travel to school by bus and another 10 students reach school through a van. Then find the relative frequency of students who reach school by bus?
Solution:
The total number of students in the above-given data set
10 + 10 + 10 = 30
Number of students traveling through bus = 10
So, the relative frequency of students traveling through bus will be = f/N = 10/30= 0.33= 33%
Problem 4: There are 36 students in a class, 20 boys and 16 girls. Then what are the frequency and relative frequency of boys in the classroom?
Solution:
The frequency of boys = Number of boys in the classroom = 20
Relative frequency of boys in classroom = Number of boys / Total students
= 20/36 = 0.5555 = 55.55 %
The frequency is 20 and the relative frequency in % is 55.55 %
Problem 5: Varun has conducted a survey in his village to study the diet habits of people. He obtained the results as given below. Then find
Diet followed | Number of people |
Vegetarian | 320 |
Mixed diet | 430 |
Non-vegetarian | 810 |
A) The relative frequency of vegetarians in Varun’s village.
B) The relative frequency of people taking a mixed diet in his village
Solution:
The relative frequency of vegetarians in Varun’s village.
Total population: 1560
Number of vegetarians: 320
From the formulaRelative frequency = Number of vegetarians / Total population
f = 320/1560
= 0.21 = 21%The relative frequency of the population taking a mixed diet in Varun’s village
Total population: 156
Number of people on mixed diet: 430
From the formulaRelative frequency = Number of population taking mixed diet/ Total population
f = 430/1560
= 0.28 = 28%