Relative Frequency Formula

The word 'relative' indicates that an event can be being considered in relation or in proportion to something else.

Frequency is a measure to predict how often a particular event occurs. The relative frequency formula helps in calculating relative frequency, which can be defined as a way to measure how often a particular event occurs against total occurrences. Let us understand the relative frequency formula using solved examples.

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What is Relative Frequency Formula?

Relative frequency can be mathematically defined as the ratio of the number of times an event occurs to the total number of events occurring in a given scenario. The following two things must be known while calculating relative frequency:

  • Number of total events/trials
  • Frequency count for a category/subgroup

\begin{aligned}
&\text { Relative Frequency } = \frac{\text { Subgroup frequency }}{\text { Total frequency }}
\end{aligned}

Or

\(\text { Relative Frequency }=\frac{f}{n}\)

where,

  • f = Number of times the data occurred in an observation
  • n = total frequencies

Relative Frequency Formula

Solved Examples Using Relative Frequency Formula

  1. Example 1: A cubical die is tossed 30 times and lands 5 times on the number 4. What is the relative frequency that the die land on the number 4?

    Solution:

    Given, number of times a die is tossed = 30
    Number of the successful trials of getting number 4 = 5
    By the relative frequency formula, we know,
    Relative frequency = Number of positive trials / Total number of trials

    \({f}=\frac{5}{30}=16.66 \%\)
     

    Answer: The relative frequency that the die would land on the number 4 is 16.66 %.

  2. Example 2: Anna has a packet containing \(20\) candies. Her favorites are the blue ones and the purple ones. The table below shows the frequency of each different candy selected as she picked all \(20\) sweets one by one and finished them all.

    Candy color Blue Purple Green Pink
    Frequency \(6\) \(6\) \(3\) \(5\)

    A) What is the relative frequency of the picked candy to be one of her favorites?

    B) What is the relative frequency for the pink candy?

    Solution

    Relative frequency = number of times an event has occurred / number of trials

    A) Relative frequency of the picked candy to be one of her favorites can be given as,

    \(=\dfrac { Frequency\hspace{2mm} of\hspace{2mm} blue + Frequency\hspace{2mm} of\hspace{2mm} purple\hspace{2mm} candy} {20} = \dfrac {12}{20} = 60\%\)

    B) Relative frequency of the pink candy can be given as,

    \(=\dfrac { Frequency\hspace{2mm}of \hspace{2mm} pink \hspace{2mm}candy} {20}\) = \(\dfrac {5}{20}\) = \(25\%\)                                                                 
    Answer: The relative frequency for Anna's favorite candy is \(60\%\) and for the pink candy it is \(25\%\).

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