RELATIVE FREQUENCY FORMULA

We come across repetitive data in a observation all the time. When a repetitive data is given, then the number of times it has been in the observation is called its frequency. Relative frequency is the comparison between the number of times a number has been repeated to the total frequencies of all the numbers. Mathematically speaking, relative frequency is the division between individual frequency of an item by the total number of repetition that has occurred.

The formula for the relative frequency is given as:

\[\large Relative\;Frequency=\frac{f}{n}\]

Here,
f is the number of times the data occurred in an observation
n  = total frequencies

Solved Example

Question: Construct the relative frequency table for the following data:
4, 1, 2, 4, 5, 1, 5, 7, 9, 0, 5, 3, 2, 5, 9, 5, 2, 3, 0, 8

Solution:

 

x f f/n
0 2 2/20 = 0.1
1 2 2/20 = 0.1
2 2 2/20 = 0.1
3 2 2/20 = 0.1
4 2 2/20 = 0.1
5 5 5/20= 0.25
6 0 0/20 = 0
7 1 1/20= 0.05
8 1 1/20= 0.05
9 2 2/20= 0.1
   n= 20

Practise This Question

There is a circular swimming pool. There is a bob at the centre of the pool at a distance of 50π m from the pool’s wall. Shyam is standing next to the

wall and holding a thread whose other end is connected to the heavy stationary bob at the centre. Holding the thread Shyam now moves along the wall for 20

seconds and the angle between the initial and final positions of the thread is 12. What is Shyam’s speed in metres/minute?