Relative Frequency Formula

Formula of Relative Frequency

For comparing the number of times a number has been repeated with the total frequencies of a number, we use the concept of relative frequency. The formula to evaluate this comparison is the relative frequency formula.

In Mathematical terms,  the formula of relative frequency is the division between individual frequencies of an item and the total number of repetition occurring.

On this page, we will understand the relative frequency distribution formula, cumulative relative frequency formula, relative probability formula, relative frequency probability formula, and the equation linking wave speed frequency and wavelength (in terms of Physics).


Relative Frequency Definition

When you toss a coin there is a fair chance of obtaining a head or a tail. However,  in some cases, in place of using equally likely outcomes, you need to use ‘relative frequency’. So, let’s understand this concept in detail.


Formula of Relative Frequency

The formula of relative frequency helps us understand the relative frequency probability formula and the relative probability formula. 

The definition of relative probability frequency formula says that we calculate the relative probability frequency by taking the count of an individual kind of outcome and divide by the total counts for all kinds of outcomes, suppose a throw of a die, or tossing a coin to get head or a tail  

Now, for understanding the relative probability formula, let’s consider an example:

Let’s suppose that a die is tossed 60 times and it lands 5 times on the number 6. What will be the relative frequency of observing the die landing on the number 6? 

Now, let’s understand how to calculate the relative frequency:

We see that the number of times a die is tossed = 60

Number of positive trials, i.e., a number of times die landed  = 5

So, the relative frequency formula is:

The number of trials turned out positive divided by the total number of trials, i.e.,

Relative frequency equation  =  n/T

f    =   5/60   =  0.083

Thus, the relative frequency of observing die landing on a floor displaying 6, 5 times is 0.083.

Now, let’s have a look at the relative frequency probability formula:


Relative Frequency Distribution Formula

For understanding the relative probability formula, we will understand the relative frequency distribution formula:

To find the relative frequency, we divide the frequency of the weight by the total number of data values. To understand how the relative frequency distribution formula works, let’s have a look at the below:


Frequency Distribution Table


Weights (in kg)

Frequency

50

10

60

12

70

5

55

13

40

10

Total

50


Now, Finding the Relative Frequency of Each


Weights (in kg)

Frequency

Relative frequency (in fraction)

Relative frequency (in %)

50

10

10/50 = 0.5

50 %

60

12

12/50 = 0.24

24 %

70

5

5/50 = 0.1

10 %

55

13

13/50 = 0.26

26 %

40

10

10/50 = 0.2

20 %

Total

50




Cumulative Relative Frequency Formula

From the above example, we understand that relative frequency is calculated by dividing the frequency of the height by the total number of data values. Now, for finding the cumulative relative frequency, we add all of the previous relative frequencies to the relative frequency for the current row and continue till we reach the last row.

For understanding how to apply the cumulative relative frequency formula, let’s suppose that the height of students in all sections of class 7 has a frequency in the  manner, as illustrated in the below table:


Apply The Cumulative Relative Frequency Formula


Height (in cm)

Frequency

Relative frequency (in fractional form)

Cumulative Relative frequency (in fraction)

Cumulative Relative frequency (in %)

150

15

15/66 = 0.28

0.28

28 %

180

13

13/66 = 0.196

0.48

46 %

1550

14

14/66 = 0.21

0.69

66 %

145

3

3/66 = 0.045

0.735

90 %

140

18

18/66 = 0.27

1.0077

100 %

Total

66





In the above table, we see that cumulative relative frequency in the last row comes out to be 1.0077 and 100% (in % form).

In Physics, we learn the terms frequency, speed, wavelength, and time to understand the properties of light; however, there is an equation linking wave speed frequency and wavelength, which is as follows:


Equation Linking Wave Speed Frequency and Wavelength

The distance a light wave travels is the wavelength, denoted by λ.

The number of times a wave repeat is a frequency, denoted by f.

We know that distance is equal to the speed over time, the same goes for the wave speed:

v  (wave speed)  =  λ/t

Also, we know that the frequency is 1/t, putting this value in the above equation:

v   =  fλ

This is the required equation linking wave speed frequency and wavelength.

Following this, we have an equation that describes the relationship between energy and wavelength equation:


Relationship Between Energy and Wavelength Equation

As the frequency and wavelength are related to light, the same is with the energy. Also, the frequency and wavelength are inversely proportional to each other, i.e., if one is shorter the other is higher, and vice versa. 

Here, the higher is the frequency of light, the higher its energy, so the relationship between energy and wavelength equation is:

E  = hv

We call this relationship the Planck-Einstein relation or the photon energy formula.

Here,

E is the photon energy in J

h  = Planck’s constant, value is 6.626 x  10-34 J.s

f = frequency in Hz or s-1                        


Conclusion

A relative frequency is the ratio of the number of times a value (magnitude) of the quantity occurs in the set of all outcomes to the total number of outcomes.

The relative frequency is used for the events that may/may not have equal outcomes that can be a throw of dice, tossing a coin, or picking up a playing card among 52.

Also, the cumulative frequency adds the value of its previous row with the current value of the relative frequency column and gives the result in the current row.

FAQs (Frequently Asked Questions)

1. How Do You Differentiate Between The Frequency And Relative Frequency?

Ans: Let's suppose that you have three ace cards – that is your frequency. You can get the frequency immediately after you proceed with your experiment without having the need to perform any calculation.

While, on the other hand, “relative frequency” is a term used to describe the number of times a result occurs upon the total number of tries.

2. What are the Absolute Frequency and Relative Frequency?

Ans: In Statistics, the frequency is known as the absolute frequency of an event. We define it as the number of times the event occurred in our experiment; however, the relative frequency comes under an empirical probability of an event that refers to the absolute frequency normalized by the total number of trials or events.

3. Is Wavelength Directly Proportional to Energy?

Ans: Yes. Electromagnetic waves possess energy and transmit their energy upon interaction with matter. The energy that EM waves possess varies directly with the frequency and is inversely proportional to wavelength. Hence, EM waves with shorter wavelengths (travels less distance) have higher energy.

4. Does Wavelength Increase With Energy?

Ans: We can measure waves by using wavelength and frequency. The wavelength is denoted by λ. The number of full wavelengths per unit of time is called the frequency (f). As a wavelength increases, its frequency, and energy (E) decrease.