Relative Frequency Formula

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

Now, Finding the Relative Frequency of Each

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

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.