RELATIVE FREQUENCY FORMULA

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The word ‘relative’ is used to indicate that an event is being considered in relation or in proportion to something else. Frequency is a way to measure how often a particular event occurs. Relative frequency, on the other hand, is a way to measure how often a particular event occurs against total occurrences. Let us learn about the relative frequency formula with few solved examples.

What Is the Relative Frequency Formula?

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.

To calculate the relative frequency two things must be known:

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

The relative frequency formula can be given as:

Relative Frequency = Subgroup frequency/ Total frequency

Or

Relative Frequency = f/ n

where,

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

Solved Examples Using Relative Frequency Formula

Example 1: A cubical die is tossed 30 times and lands 5 times on the number 6. What is the relative frequency of observing the die land on the number 6?

Solution: Given, number of times a die is tossed = 30
Number of the successful trials of getting number 6 = 5
By the formula, we know,
Relative frequency = Number of positive trial / Total number of trials
f = 5/ 30 = 16.66%

Answer: The relative frequency of observing the die land on the number 6 is 16.66%

Example 2: Anna has a packet containing 20 candies. Her favorites are the yellow ones and the red 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 colorYellowRedGreenBrown
Frequency6635

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

B) What is the relative frequency for the brown 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:

(Frequency of yellow + Frequency of red candy)/ 20 = 12/ 20 = 60%

B) Relative frequency of the brown candy

Frequency of brown candy/ 20 = 5/ 20 = 25%                        

Answer:  60% and 25%

Example 3: A coin is flipped 100 times, the coin lands on heads 48 times. What is the relative frequency of the coin landing on tails?

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

The event in consideration is the coin landing on tails = 100 – 48 = 52 times

Relative frequency of the coin landing on tails = 52/100 = 0.52 = 52%

Answer: Relative frequency of the coin landing on tails is 52%.

FAQs on Relative Frequency Formula

What Is Relative Frequency Formula?

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario. The relative frequency formula is given as: Relative Frequency = Subgroup frequency/ Total frequency.

Maxwell and his wife, Rebecca, argue over which birdseed brand to put in their bird feeder. Maxwell claims they should use Brand A, which is cost-effective. Rebecca agrees that Brand A is cheaper but argues that it is only cheaper because it has a higher proportion of filler seeds that the birds would not eat. Therefore, she thinks they should purchase Brand B, as less will go to waste. To test the validity of her claim, Rebecca and Maxwell buy a bag of each brand and count the number of filler seeds in the mix. The number of filler seeds counted within the mix represents the frequency (or absolute frequency) of filler seeds. A frequency is an observable count of a specific variable response type.

After counting, Maxwell reports that Brand A has 150 filler seeds while brand B has 200. Based on these numbers, Maxwell claims that Brand B is not the better value, as it contains a higher number of filler components. While this is true, Maxwell has not considered the concept of relative frequency. What is a relative frequency? By definition, relative frequency is the number of times a variable response type is counted in relation to the total number of responses. If the number of total seeds differs between bad A and B, then the proportion of filler seeds will vary between each brand. This is why researchers are often interested in how a response variable’s relative frequency (rather than the absolute frequency) changes between sample groups.

What’s the Difference Between Frequency and Relative Frequency?

An easy way to define the difference between frequency and relative frequency is that frequency relies on the actual values of each class in a statistical data set while relative frequency compares these individual values to the overall totals of all classes concerned in a data set.

Is Relative Frequency and Probability the Same?

A relative frequency is found on the basis of the experimental probability. The probability is a number between 0 and 1.0 indicating the likelihood of an event. This defines probability as the number of times an event occurs divided by the number of opportunities for it to occur. The result of this calculation is called the “relative frequency” of the event.

Is Relative Frequency a Percentage?

A relative frequency count is a measure of the number of times that an event occurs out of the total events. It can be expressed as a proportion. It is also often expressed as a percentage

Relative Frequency

The number of times an event occurs is called a frequency. Relative frequency is an experimental one, but not a theoretical one. Since it is an experimental one, it is possible to obtain different relative frequencies when we repeat the experiments. To calculate the frequency we need

  • Frequency count for the total population
  • Frequency count for a subgroup of the population

We can find the relative frequency probability in the following way if we know the above two frequencies. The formula for a subgroup is;

Relative Frequency = Subgroup Count / Total Count

How to Calculate Relative Frequency?

The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes gives the value of relative frequency.

Let’s understand the Relative Frequency formula with the help of an example

Let’s look at the table below to see how the weights of the people are distributed.

Step 1: To convert the frequencies into relative frequencies, we need to do the following steps.

Step 2: Divide the given frequency bt the total N i.e 40 in the above case(Total sum of all frequencies).

Step 3 : Divide the frequency by total number Let’s see how : 1/ 40 = 0.25.

Example: Let us solve a few more examples to understand the concepts better.

This is a frequency table to see how many students have got marks between given intervals in Maths.

MarksFrequencyRelative Frequency
45 – 5033 / 40 x 100 = 0.075
50 – 5511 / 40 x 100 = 0.025
55 – 6011 / 40 x 100 = 0.075
60 -6566 / 40 x 100 = 0.15
65 – 7088 / 40 x 100 = 0.2
70 – 8033 / 40 x 100 = 0.275
80 -901111 / 40 x 100 = 0.075
90 – 10071 / 40 x 100 = 0.025

It is necessary to know the disparity between the theoretical probability of an event and the observed relative frequency of the event in test trials. The theoretical probability is a number which is calculated when we have sufficient information about the test. If each probable outcome in the sample space is equally likely, then we can consider the number of outcomes of a happening and the number of outcomes in the sample space to calculate the theoretical probability.

The relative frequency is dependent on the series of outcomes resulted in while doing statistical analysis. This frequency can be varied every time we repeat the experiment. The more tests we do during an experiment, the observed relative frequency of an event will get closer to the theoretical probability of the event.

Cumulative Relative Frequency

Cumulative relative frequency is the accumulation of the previous relative frequencies. To obtain that, add all the previous relative frequencies to the current relative frequency. The last value is equal to the total of all the observations. Because all the previous frequencies are already added to the previous total.

Relative Frequency Examples

Example 1: A die is tossed 40 times and lands 6 times on the number 4. What is the relative frequency of observing the die land on the number 4? 

Solution: Given, Number of times a die is tossed = 40

Number of positive trial = 6

By the formula, we know,

Relative frequency = Number of positive trial/Total Number of trials

f = 6/40 = 0.15

Hence, the relative frequency of observing the die land on the number 4 is 0.15

Example 2: A coin is tossed 20 times and lands 15 time on heads. What is the relative frequency of observing the coin land on heads?

Solution: Total number of trials = 20

Number of positive trails = 15

By the formula, we know,

Relative frequency = Number of positive trial/Total Number of trials

f = 15/20 = 0.75

Hence, the relative frequency of observing the coin land on heads is 0.75

All the Relative Frequencies add up to 1 (except for any rounding error).

Relative Frequency Distribution: Definition and Examples

What is a Relative frequency distribution?

A relative frequency distribution is a type of frequency distribution.

The first image here is a frequency distribution table. A frequency distribution table shows how often something happens. In this particular table, the counts are how many people use certain types of contraception.

A frequency distribution table.

With a relative frequency distribution, we don’t want to know the counts. We want to know the percentages. In other words, what percentage of people used a particular form of contraception?

This relative frequency distribution table shows how people’s heights are distributed.

Note that in the right column, the frequencies (counts) have been turned into relative frequencies (percents). How you do this:

  1. Count the total number of items. In this chart the total is 40.
  2. Divide the count (the frequency) by the total number. For example, 1/40 = .025 or 3/40 = .075.

This information can also be turned into a frequency distribution chart. This chart shows the relative frequency distribution table and the frequency distribution chart for the information. How to we know it’s a frequency chart and not a relative frequency chart? Look at the vertical axis: it lists “frequency” and has the counts:

This next chart is a relative frequency histogram. You know it’s a relative frequency distribution for two reasons:

  1. It’s labeled as relative frequency (which all good charts should be!).
  2. The vertical axis has percentages (as decimals, .1, .2, 3 …)instead of counts (1, 2, 3…).
Chart showing how book sales compare to each other as percentages of a whole.

How to Make a Relative Frequency Table

Making a relative frequency table is a two step process.
Step 1: Make a table with the category names and counts.

Step 2: Add a second column called “relative frequency”. I shortened it to rel. freq. here for space.

Step 3: Figure out your first relative frequency by dividing the count by the total. For the category of dogs we have 16 out of 56, so 16/56=0.29.

Step 4: Complete the rest of the table by figuring out the remaining relative frequencies.
Cats = 28 / 56 = .5
Fish = 8 / 56 = .14
Other = 4 / 56 = 0.07
Don’t forget to put the total at the bottom of the rel. freq. column: .29 + .5 + .14 +.07 = 1.
Note: The usual way to complete the table is with decimals or percents. However, it’s still technically correct to just leave the ratios (i.e. 28/56) in the column (that way you don’t have to do the math!).

Cumulative Relative Frequency

To find the cumulative relative frequency, follow the steps above to create a relative frequency distribution table. As a final step, add up the relative frequencies in another column. Here’s the column to the right is labeled “cum. rel. freq.”)

The first entry in the column is the same as the first entry in the rel.freq column (.29).
Next, I added the first and second entries to get 0.29 + 0.50 = 0.79.
Next, I added the first, second and third entries to get 0.29 + 0.50 + 0.14 = 0.93.
Finally, I added the first, second, third and fourth entries to get 0.29 + 0.50 + 0.14 + 0.07 = 1.

Relationship Between Relative Frequency and Probability

Probability is the chance that a particular outcome will happen. For instance, flipping a coin has a 1/2 probability of landing on “heads” and a 1/2 probability of landing on “tails.” An outcome’s probability and its relative frequency can be similar or very different. Based on a coin flip, 50 out of every 100 flips should be heads. However, after flipping a biased coin, one might find that only 30 out of 100 flips are heads. This may indicate that further research is needed to understand other influences impacting a coin flip.

Relative frequency should be at or very close to a known probability as the number of repetitions is increased. If a coin is only flipped twice, it is reasonable to think that it may land on heads both times. However, what if the number of coin flips was increased to 1,000? The likelihood that all 1,000 flips would land on heads with an unbiased coin is doubtful. For this reason, researchers should aim to add many repetitions to their study to get or support an accurate probability for a variable response type.

How to Find Relative Frequency

To find the relative frequency of an outcome, investigators must know the frequency of the preferred outcome and the total number of outcomes. The relationship between these two variables is expressed in the following relative frequency formula, where “f” is the frequency of a specific outcome, while “n” is the total number of responses:

Frelative=f/n

Relative Frequency Equation Example

The following example demonstrates finding the relative frequency of a specific variable response type. Maria wants to bake cookies and asks her friends what flavor she should bake. Out of 30 friends, 13 suggest chocolate chips, while 17 of them suggest snickerdoodles. If Maria were interested in the relative frequency of “chocolate chip” given as a response, she would plug her data into the relative frequency equation as such:

Frelative=13/30

The relative frequency of “chocolate chip” as a response type was 0.43.

What is the relative frequency in statistics?

The relative frequency definition is the number of times an event occurs during experiments divided by the number of total trials conducted. In other words, it tells you how often something happens compared to all outcomes. This is why it’s relative – we consider it in proportion to something else.

You can encounter other terms used interchangeably with relative frequency, such as experimental probability or empirical probability. This may cause confusion: is this the probability we usually talk about? Not really; this term is customarily used to refer to the theoretical probability. Therefore, it may be a good idea to compare these two quantities.

What’s the difference between experimental and theoretical probability?

Experimental probability is the estimated likelihood of a particular outcome based on repeated observations; in other words, something that actually happened. Theoretical probability tells us what should happen if the results were purely theoretical.

For example, if you flip a coin, the chances of landing on either side are exactly 50/50 – theoretically. However, if you tossed a coin 100 times, it’s unlikely that you’d get 50 tails. This is where the relative frequency formula comes in handy. Interestingly enough, the more trials you conduct, the closer the experimental value will be to the theoretical probability. It also works the same way for scenarios with more possible outcomes, such as rolling dice.

How to calculate relative frequency?

Using the relative frequency equation isn’t very difficult, as you’re about to find out. If you have observational data, divide the number of occurrences of the outcome you’re interested in by the number of all occurrences. Mathematically, we can write this as:

relative frequency = frequency of the desired outcome / all occurrences.

As you may have guessed, the result is a fraction.

Often, you’ll find yourself calculating the experimental probability for every sample. This can help you find the cumulative relative frequency, as well as prepare the relative frequency diagram (which shows the frequency distribution). You may also want to find the conditional relative frequency that how many data points share a certain characteristic.

How to find the relative frequency with the relative frequency calculator?

Although the relative frequency formula is rather simple, calculating things by hand may be tedious, especially if you have to work with a lot of data. So, how to use the relative frequency calculator to make your work more efficient?

  1. Choose between grouped and ungrouped data. The difference is that ungrouped data deals with individual points, whereas grouped data considers intervals. It impacts the way the calculations are handled: you can see the difference if you compare standard deviation and grouped data standard deviation.
  2. If the data is ungrouped, simply input the consecutive data points. If the data is grouped, you’ll need to input the starting (smallest) value and the interval size, which is the number of data points in every interval. After that, all you need to do is input the data points, and the calculator will separate them and consider them as intervals.
  3. Choose the type of graph, and the calculator will construct a relative frequency distribution table and diagram for you. It can represent either regular or cumulative relative frequency.

Additionally, the calculator will provide you with other statistical data, such as the mean!

Relative frequency meaning, applications and relative frequency table

Numbers and formulae are hardly ever of any use for us without context. When could you possibly use the relative frequency equation? It turns out that sports can serve as an excellent, real-life example.

In this case, we will consider a particular Team X from one of the top soccer leagues. When their top player left in 2018, their rivals must’ve started to feel a bit more hopeful about their future encounters. Imagine that you’re the manager of another team at that time, and you’re 11 weeks into the season — time to analyze Team X’s form before facing them.

It seems that Team X has won 5 matches, lost 4, and 2 ended in a draw so far. Therefore, their empirical probability of losing is 4/11 as they lost 4 out of 11 games played. If you decide that anything is better than being defeated, you can find the cumulative relative frequency of Team X’s loses and draws. Adding both of these values yields 6/11. You can convert this fraction to a percentage to obtain approximately 54.5%.

To present it graphically to the players, you could construct a relative frequency distribution table:

Team X’s resultRelative frequency
Win5/11
Draw2/11
Loss4/11

Of course, there are many other factors to consider, such as tactics, your team’s condition – measurable, for example, with VO2 max – or even just basic luck. However, we hope that this example has shown you how applicable relative frequency can be.

FAQ

What is frequency in math?

Frequency in statistics is defined as the number of times a certain observation occurs in a dataset. There are several types of frequencies, such as:

  • Absolute frequency;
  • Cumulative frequency;
  • Relative frequency; and
  • Relative cumulative frequency.

How to calculate relative frequency percentage?

To find the relative frequency percentage:

  1. Find the relative frequency. It should be expressed as a fraction by default.
  2. Convert it to a decimal.
  3. Multiply by 100.
  4. Congratulations! You found the relative frequency percentage!

How do I calculate cumulative relative frequency?

Here’s how to find cumulative relative frequency:

  1. Find the experimental probability for every item in the dataset using the relative frequency formula. It may be helpful to build a relative frequency table.
  2. Add the relative frequencies of previous data points to the relative frequency of the current item.
  3. The cumulative relative frequency of the last entry should be equal to 1.0. It means that 100% of the data has been accumulated.

What is a relative frequency table?

A relative frequency table is a chart that shows experimental probabilities for a certain type of data based on the population sampled. Their values are usually represented as decimal fractions rather than percentages.

What is the difference between relative frequency and cumulative frequency?

Cumulative frequency is a sum of the frequencies of an item and all previous data points. Relative frequency definition is a fraction showing how often an item appears compared to all other objects. However, you can also calculate cumulative relative frequency that combines both ideas.

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