Relative Frequency

Introduction

Relative frequency is the number of times an event occurs divided by the total number of occurrences that occur in a given situation. A count of a specific event is called a frequency. For instance, Kim read ten books on statistics this year. The football team picked up 11 victories. Relative frequencies, on the other hand, do not employ raw counts. Instead, they use percentages, proportions, or fractions to compare the count for one type of event to the entire number of events. The word "relative" refers to a specific tally in relation to the overall number, which is where it is used. Kim, for instance, read 35% of his books about statistics. 75 percent of the football team's games were victories, etc.

What is Frequency?

Frequency of a data point in provided data is the number of times the data point is repeated in data. For example 25 students score 50 marks, here 25 is the frequency of the score 50.

Types of Frequency

The following are the types of frequency in frequency distribution −

• Grouped frequency distribution.

• Ungrouped frequency distribution.

• Cumulative frequency distribution.

• Relative frequency distribution.

• Relative cumulative frequency distribution.

Relative Frequency

The ratio of the number of times an event occurs to total number of events occurring in a scenario is known as relative frequency. Two facts must be known in order to determine the relative frequency −

• Total number of occasions/trials

• Frequency count for a subset or category

How to calculate Relative Frequency?

We use following formula to determine the relative frequency −

$$\mathrm{Relative\:Frequency\:=\:\frac{subgroup\:frequency}{total\:Frequency}}$$

Or

$$\mathrm{Relative\:Frequency\:=\:\frac{f}{N}}$$

where 𝑓 = number of times the data occurred in observation and 𝑁 is total frequency.

Mean, Median and Mode by Relative Frequency

To find the average (Mean) without needing to divide, multiply the numbers by their respective relative frequencies first, then add the results. The middle value in an ordered set of data is known as the median. The observations are already sorted in ascending order in a frequency table. By searching for the value in the centre place, we can find the median. The median is the number in the centre when there are an odd number of observations. A frequency table is a graph that displays the prevalence or typical distribution of a particular kind of data. The frequency that an event occurs inside a particular context is what we are examining when we look at a frequency. A chart that displays the prevalence or pattern of a particular piece of data based on the population sampled is known as a relative frequency table. In order to calculate relative frequency, we must first determine how frequently a certain event occurs in relation to all other events.

Solved Examples

What is the frequency and relative frequency of winning if an Indian cricket team has won 8 out of a total of 10 games?

Answer − From a total of 10, an Indian cricket team has won 8, making the frequency of winning 8 and the relative frequency of winning $\mathrm{\frac{8}{10}}$

2)A die is tossed 20 times and turned 6, 5 times on the face. What is the relative frequency of observing the die turned on the number 6?

Answer − Dice is thrown 20 times in the given experiment

5 successful attempts at putting the number 6 on one's face

Using the formula of relative frequency, we get

$\mathrm{Relative\:frequency\:=\:\frac{no.\:of\:positive\:trial}{total\:no.\:of\:trials}\:=\:\frac{5}{20}\:=\:\frac{1}{4}\:=\:0.25\:=\:25\%}$

3)When a coin is flipped 50 times, 18 times it lands on heads. What percentage of the time does the coin land on its tails?

Answer − Coin is thrown 50 times in the given experiment

$\mathrm{50\:-\:18\:=\:32}$ successful attempts at putting the coin to land on tail

Using the formula of relative frequency, we get

$\mathrm{Relative\:frequency\:=\:\frac{no.\:of\:positive\:trial}{total\:no.\:of\:trials}\:=\:\frac{32}{50}\:=\:\frac{16}{25}\:=\:64\%}$

4)When a coin is thrown 200 times, 150 times it lands on tails. What percentage of the time does the coin land on its tails?

Answer − Coin is thrown 200 times in the given experiment.

150 successful attempts at putting the coin to land on tail

Using the formula of relative frequency, we get

$\mathrm{Relative\:frequency\:=\:\frac{no.\:of\:positive\:trial}{total\:no.\:of\:trials}\:=\:\frac{150}{200}\:=\:\frac{15}{20}\:=\:75\%}$

5)When a dice is flipped 50 times, 30 times it lands on number 5. What percentage of the time does the coin land on its 5?

Answer − Dice is thrown 50 times in the given experiment.

30 successful attempts at putting the number 5 on one's face.

By the formula of relative frequency, we know,

$\mathrm{Relative\:frequency\:=\:\frac{no.\:of\:positive\:trial}{total\:no.\:of\:trials}\:=\:\frac{30}{50}\:=\:\frac{3}{5}\:=\:60\%}$

Conclusion

Relative frequency is the number of times an event occurs divided by the total number of occurrences that occur in a given situation. Relative means anything compared to or in proportion to another object. We use the following formula to determine the relative frequency:

$$\mathrm{Relative\:frequency\:=\:\frac{subgroup\:frequency}{total\:frequency}}$$

FAQs

1. What is meant by the term relative?

Relative means anything compared to or in proportion to another object.

2. What is the frequency term in statistics?

: Frequency of a data point in provided data is the number of times the data point is repeated in data.

3. Define the term relative frequency connected to term frequency?

The quantity of occurrences of an event is referred to as its frequency. The concept of relative frequency is experimental rather than theoretical. It is experimental, therefore if we repeat the trials, we can get different relative frequencies

4. What foundation does relative frequency have?

A relative frequency describes how frequently a particular kind of event happens among all observations. It is a kind of frequency that employs fractions, percentages, and proportions.

5. Is probability the same as relative frequency?

The relative frequency is a more accurate measure of probability the more times an experiment has been run

6. What impact does a higher trial count have on relative frequency?

The relative frequency swings less and approaches the theoretical probability as the number of trials rises.

7. Why don't we just use frequency like we used to?

The difference between frequency and relative frequency can be explained by noting that whereas relative frequency compares these individual values to the sums of all the classes involved in the data set, frequency depends on the actual values of each class in a statistical data set

8. Is relative frequency a decimal?

Relative frequencies can be written as fractions, percent, or decimals.

9. What are the three different frequency distribution types?

Cumulative frequency distribution, relative frequency distribution, and relative cumulative frequency distribution are the three different frequency distribution types.

10. What is a frequency curve?

A frequency curve is a straight line that represents the limiting case of a histogram calculated for a frequency distribution of a continuous distribution as the number of data points rises sufficiently

11. What is it called when a frequency distribution is not symmetrical?

If a distribution is not symmetric with zero skewness—that is, if it does not skew—it is said to be asymmetric. The skewness of an asymmetric distribution might be left or right. The left tail is longer in a left-skewed distribution, also referred to as a negative distribution.

12. What does the kurtosis signify?

Kurtosis is a statistical metric that expresses how drastically a distribution's tails diverge from those of a normal distribution. Kurtosis, thus, determines if a particular distribution's tails contain extreme values.