relative frequencies assignment

Relative Frequency

Learn how to calculate relative frequency., relative frequency lesson, what is relative frequency.

Relative frequency is how often something occurs. The general formula for relative frequency is given as:

• Relative frequency = event count/total count

Since we divide how many times the event occurs by the total number of events that occurred, the frequency of the event is relative to the total number of events .

Using the relative frequency formula will always result in a decimal value ranging from 0 to 1. A relative frequency of 0 means the event never occurs. A relative frequency of 1 means the event occurs every time.

Why use Relative Frequency?

Calculating relative frequency of an event can help us understand the event and predict the future. If we know that an event has happened 55% of the time in the past and we are calculating that from a sufficient data pool, we can predict that the event has roughly a 55% chance of happening in the future.

Often times we won't need to predict an exact percentage chance an event has of happening in the future and can instead make a general prediction. For example, as of May 2023, an NBA team has never come back from a 0-3 deficit in the playoffs to win the series. If we plug the data into our formula, we will get a relative frequency of 0.

Based on this frequency, we can definitely predict that it is unlikely an NBA team comes back from a 0-3 deficit in the playoffs to win a series! But we also must remember that we calculated relative frequency to make this prediction, so it is not impossible that an NBA team comes back from a 0-3 deficit in the playoffs to win a series sometime in the future. Relative frequency is a calculation of how likely something is to happen based on previous results. It is not a guarantee that something will or will not happen.

How to Calculate Relative Frequency: Example Problem

A person opens their fridge door 17 times on a particular day. A bottle of ketchup falls out on 4 occasions. What is the relative frequency of the bottle of ketchup falling out when their fridge door is opened?

• The total count is 17, and the event count is 4. Let's plug these values into the relative frequency general formula.
• Relative frequency = 4/17 = 0.2353
• Converting the relative frequency to a percentage:
• 100·0.2353 = 23.53%
• The relative frequency is 0.2353, or 23.53%.

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Statistics By Jim

Making statistics intuitive

Relative Frequencies and Their Distributions

By Jim Frost 5 Comments

A relative frequency indicates how often a specific kind of event occurs within the total number of observations. It is a type of frequency that uses percentages, proportions, and fractions.

In this post, learn about relative frequencies, the relative frequency distribution, and its cumulative counterpart.

Frequencies vs. Relative Frequencies

A frequency is a count of a particular event. For example, Jim read ten statistics books this year. The football team won 12 games. For more information, read my post about frequency tables .

In contrast, relative frequencies do not use raw counts. Instead, they relate the count for a particular type of event to the total number of events using percentages, proportions, or fractions. That’s where the term “relative” comes in—a specific tally relative to the total number. For instance, 25% of the books Jim read were about statistics. The football team won 85% of its games.

If you see a count, it’s a frequency. If you see a percentage, proportion, ratio, or fraction, it’s a relative frequency.

Relative frequencies help you place a type of event into a larger context. For example, a survey indicates that 20 students like their statistics course the most. From this raw count, you don’t know if that’s a large or small proportion. However, if you knew that 30 out of 40 (75%) respondents indicated that statistics was their favorite, you’d consider it a high number!

Additionally, they allow you to compare values between studies. Imagine that different sized schools surveyed their students and obtained different numbers of respondents. If 30 students indicate that statistics is their favorite, that could be a high percentage in one school but a low percentage in another, depending on the total number of responses.

Relative frequencies facilitate apples-to-apples comparisons.

Learn more about percentages in my posts, How to Calculate a Percentage , Percent Change and Percent Error .

How to Find a Relative Frequency

To calculate relative frequencies, you must know both of the following:

• The count of events for a category.
• The total number of events.

Relative frequency calculations convert counts into percentages by taking the count of a specific type of event and dividing it by the total number of observations. Its formula is the following:

For example, imagine a school surveys 50 students and asks them to name their favorite course. Thirty-six students state that statistics is their favorite.

• The frequency of “statistics” responses is 36.
• The total number of responses is 50.

To find the relative frequency for the statistics course, perform the following division: 36 / 50 = 72%.

Relative Frequencies as Empirical Probabilities

Relative frequencies also serve as empirical probabilities. Probabilities define the likelihood of events occurring. Probability calculations often rely heavily on theory. However, when you observe the relative frequency of an event, it’s an empirical probability. In other words, analysts calculate them using real-world observations rather than theory.

An empirical probability is the number of events out of the total number of observations.

Related post : Probability Fundamentals

Relative Frequency Distributions: Tables and Graphs

A relative frequency distribution describes the relative frequencies for all possible outcomes in a study. While a single value is for one type of event, the distribution displays percentages for all possible results. Analysts typically present these distributions using tables and bar charts.

When you’re assessing two categorical variables together, you can use relative frequencies in a contingency table. Learn more about Contingency Tables: Definition, Examples & Interpreting .

Let’s bring them to life by working through an example!

Table example

The relative frequency distribution table below displays the percentage of students in each grade at a small school with 88 students.

If the table had only the first two columns, grade level and count of students, it would be a frequency distribution. A frequency distribution describes the counts for all possible outcomes. It’s the percentage column that makes it a relative frequency distribution. You can see how the two types of distributions are related.

To create a relative frequency distribution table, take the count of students in a row (one grade level) and divide it by the total number of students. For example, in the first row, there are 23 students in the first grade—23 out of 88 = 26.1%. For second graders, it’s 20 out of 88 = 22.7% Repeat this process for all rows in the table.

Because these tables consider all possible outcomes, the total percentage must sum to 100%, excepting rounding error.

They are handy because you instantly know the percentage of the total for each outcome, and you can identify trends and patterns. For example, first graders account for just over a quarter (26.1%) of the entire school by themselves. Conversely, 6 th graders make up only 9.1% of the school. There’s a downward trend in values as grade levels increase.

Bar chart example

You can also use bar charts to display relative frequency distributions. The graph below depicts the same information as the table. It shows a clear trend for the upper grades to have smaller percentages of total students.

Related post : Bar Charts: Using, Examples, and Interpreting

Cumulative Relative Frequency Distributions

A cumulative relative frequency distribution sums the progression of relative frequencies through all the possible outcomes. Creating this type of distribution entails adding one more column to the table and summing the values as you move down the rows to create a running, cumulative total.

For this example, we’ll return to school students. The cumulative relative frequency table below adds the final column.

To find the cumulative value for each row, sum the relative frequencies as you work your way down the rows. The first value in the cumulative row equals that row’s relative frequency. For the 2 nd row, add that row’s value to the previous row. In the table, we add 26.1 + 22.7 = 48.8%. In the third row, add 17% to the previous cumulative value, 17 + 48.8 = 65.8%. And so on through all the rows.

The final cumulative value must equal 1 or 100%, excepting rounding error.

You can also display cumulative relative frequency distributions on graphs. In the chart below, I added the orange cumulative line. Use these cumulative distributions to determine where most of the events/observations occur. In the example data, the first and second graders comprise about half the school.

Benford’s law is a fascinating relative frequency distribution that describes how often numbers in datasets start with each digit from 1 to 9. Learn more about Benford’s law and its distribution .

To learn about functions that describe distributions, read my post, Understanding Probability Distributions .

Related post : Cumulative Frequency: Finding & Interpreting

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Reader Interactions

April 23, 2022 at 2:26 am

How do you get the actual frequency from the relative frequency.

September 9, 2021 at 2:35 am

Good article on basics. Can be related to the Pareto chart. Similarly another application of this in “P” chart also would be useful which is also used as control charts in industries.

September 7, 2021 at 9:00 am

September 7, 2021 at 3:16 am

Thanks Jim, your post is too helpful, now am well understanding the relative frequency and its importance.

September 7, 2021 at 11:55 pm

You’re very welcome, Josephine!

Comments and Questions Cancel reply

Relative Frequency

How often something happens divided by all outcomes.

Example: Your team has won 9 games from a total of 12 games played:

• the Frequency of winning is 9
• the Relative Frequency of winning is 9/12 = 75%

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

Example: Travel Survey

92 people were asked how they got to work:

• 35 used a car
• 42 took public transport
• 8 rode a bicycle

The Relative Frequencies (to 2 decimal places) are:

• Car: 35/92 = 0.38
• Public Transport: 42/92 = 0.46
• Bicycle: 8/92 = 0.09
• Walking: 7/92 = 0.08

0.38+0.46+0.09+0.08 = 1.01

(It would be exactly 1 if we had used perfect accuracy)

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How to Calculate Relative Frequency

Last Updated: May 26, 2023 Fact Checked

This article was reviewed by Joseph Meyer . Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 123,796 times.

Absolute frequency is a simple concept to grasp: it refers to the number of times a particular value appears in a specific data set (a collection of objects or values). However, relative frequency can be a little trickier. It refers to the proportion of times a particular value appears in a specific data set. In other words, relative frequency is, in essence, how many times a given event occurs divided by the total number of outcomes. If you organize your data, calculating and presenting relative frequency can become a simple task.

Preparing the Data

• For example, suppose you are collecting data on the ages of people who attend a particular movie. You could decide to collect and report the exact age of everyone who attends. But this is likely to give you 60 or 70 different results, being every number from about 10 through 70 or 80. You may instead wish to collect data in groups, like “Under 20,” “20-29,” “30-39,” “40-49,” “50-59,” and “60 plus.” This would be a more manageable set of six data groups.
• As another example, a doctor might collect body temperatures of patients on a given day. In this case, just collecting whole numbers, like 97, 98, 99, might not be precise enough. It might be necessary to report data in decimals in this case.

• When you are sorting and rewriting your collection of data, be careful to include every point correctly. Count the data set to make sure you do not leave off any values.

Calculating Relative Frequency Results

• In the sample data set provided above, counting each item results in 16 total data points.

Reporting Relative Frequency Data

• For example, using the data set above, the relative frequency table would appear as follows:
• x : n(x) : P(x)
• 1 : 3 : 0.19
• 2 : 1 : 0.06
• 3 : 2 : 0.13
• 4 : 3 : 0.19
• 5 : 4 : 0.25
• 6 : 2 : 0.13
• 7 : 1 : 0.06
• total : 16 : 1.01

• For example, the sample data set you have been working with includes all values from 1 to 7. But suppose that the number 3 never appeared. That could be important, and you would report the relative frequency of the value 3 as 0.

• For example, the decimal result of 0.13 is equal to 13%.
• The decimal result of 0.06 is equal to 6%. (Don’t just skip over the 0.)

Calculator, Practice Problems, and Answers

Community Q&A

• Physically speaking, the relative frequency tells you the presence or occurrence of a particular event in a set of events. Thanks Helpful 0 Not Helpful 0
• If you add up the relative frequencies of all items in a data set, you should get a sum of 1. If you round off your values, the sum may not be exactly 1.0. Thanks Helpful 0 Not Helpful 0
• If your data set is too large for simple counting, you may need to use a software package like MS-Excel or MATLAB to avoid mistakes. Thanks Helpful 0 Not Helpful 0

You Might Also Like

• ↑ https://www.mathsisfun.com/data/relative-frequency.html
• ↑ https://openstax.org/books/statistics/pages/1-3-frequency-frequency-tables-and-levels-of-measurement
• ↑ https://www.omnicalculator.com/statistics/relative-frequency
• ↑ https://www.cuemath.com/relative-frequency-formula/

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2.4 - how to assign probability to events.

We know that probability is a number between 0 and 1. How does an event get assigned a particular probability value? Well, there are three ways of doing so:

• the personal opinion approach
• the relative frequency approach
• the classical approach

On this page, we'll take a look at each approach.

The Personal Opinion Approach Section  

This approach is the simplest in practice, but therefore it also the least reliable. You might think of it as the "whatever it is to you" approach. Here are some examples:

• "I think there is an 80% chance of rain today."
• "I think there is a 50% chance that the world's oil reserves will be depleted by the year 2100."
• "I think there is a 1% chance that the men's basketball team will end up in the Final Four sometime this decade."

Example 2-4 Section  

At which end of the probability scale would you put the probability that:

• one day you will die?
• you can swim around the world in 30 hours?
• you will win the lottery someday?
• a randomly selected student will get an A in this course?
• you will get an A in this course?

The Relative Frequency Approach Section  

The relative frequency approach involves taking the follow three steps in order to determine P ( A ), the probability of an event A :

• Perform an experiment a large number of times, n , say.
• Count the number of times the event A of interest occurs, call the number N ( A ), say.
• Then, the probability of event A equals:

\(P(A)=\dfrac{N(A)}{n}\)

The relative frequency approach is useful when the classical approach that is described next can't be used.

Example 2-5 Section  

When you toss a fair coin with one side designated as a "head" and the other side designated as a "tail", what is the probability of getting a head?

I think you all might instinctively reply \(\dfrac{1}{2}\). Of course, right? Well, there are three people who once felt compelled to determine the probability of getting a head using the relative frequency approach:

As you can see, the relative frequency approach yields a pretty good approximation to the 0.50 probability that we would all expect of a fair coin. Perhaps this example also illustrates the large number of times an experiment has to be conducted in order to get reliable results when using the relative frequency approach.

By the way, Count Buffon (1707-1788) was a French naturalist and mathematician who often pondered interesting probability problems. His most famous question

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?

came to be known as Buffon's needle problem. Karl Pearson (1857-1936) effectively established the field of mathematical statistics. And, once you hear John Kerrich's story, you might understand why he, of all people, carried out such a mind-numbing experiment. He was an English mathematician who was lecturing at the University of Copenhagen when World War II broke out. He was arrested by the Germans and spent the war interned in a prison camp in Denmark. To help pass the time he performed a number of probability experiments, such as this coin-tossing one.

Example 2-6 Section  

Some trees in a forest were showing signs of disease. A random sample of 200 trees of various sizes was examined yielding the following results:

What is the probability that one tree selected at random is large?

There are 68 large trees out of 200 total trees, so the relative frequency approach would tell us that the probability that a tree selected at random is large is 68/200 = 0.34.

What is the probability that one tree selected at random is diseased?

There are 37 diseased trees out of 200 total trees, so the relative frequency approach would tell us that the probability that a tree selected at random is diseased is 37/200 = 0.185.

What is the probability that one tree selected at random is both small and diseased?

There are 8 small, diseased trees out of 200 total trees, so the relative frequency approach would tell us that the probability that a tree selected at random is small and diseased is 8/200 = 0.04.

What is the probability that one tree selected at random is either small or disease-free?

There are 121 trees (35 + 46 + 24 + 8 + 8) out of 200 total trees that are either small or disease-free, so the relative frequency approach would tell us that the probability that a tree selected at random is either small or disease-free is 121/200 = 0.605.

What is the probability that one tree selected at random from the population of medium trees is doubtful of disease?

There are 92 medium trees in the sample. Of those 92 medium trees, 32 have been identified as being doubtful of disease. Therefore, the relative frequency approach would tell us that the probability that a medium tree selected at random is doubtful of disease is 32/92 = 0.348.

The Classical Approach Section  

The classical approach is the method that we will investigate quite extensively in the next lesson. As long as the outcomes in the sample space are equally likely (!!!), the probability of event \(A\) is:

\(P(A)=\dfrac{N(A)}{N(\mathbf{S})}\)

where \(N(A)\) is the number of elements in the event \(A\), and \(N(\mathbf{S})\) is the number of elements in the sample space \(\mathbf{S}\). Let's take a look at an example.

Example 2-7 Section  

Suppose you draw one card at random from a standard deck of 52 cards. Recall that a standard deck of cards contains 13 face values (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King) in 4 different suits (Clubs, Diamonds, Hearts, and Spades) for a total of 52 cards. Assume the cards were manufactured to ensure that each outcome is equally likely with a probability of 1/52. Let \(A\) be the event that the card drawn is a 2, 3, or 7. Let \(B\) be the event that the card is a 2 of hearts (H), 3 of diamonds (D), 8 of spades (S) or king of clubs (C). That is:

• \(A= \{x: x \text{ is a }2, 3,\text{ or }7\}\)
• \(B = \{x: x\text{ is 2H, 3D, 8S, or KC}\}\)
• What is the probability that a 2, 3, or 7 is drawn?
• What is the probability that the card is a 2 of hearts, 3 of diamonds, 8 of spades or king of clubs?
• What is the probability that the card is either a 2, 3, or 7 or a 2 of hearts, 3 of diamonds, 8 of spades or king of clubs?
• What is \(P(A\cap B)\)?

Relative Frequency Calculator

What is the relative frequency in statistics.

• What's the difference between experimental and theoretical probability?

How to calculate relative frequency?

How to find the relative frequency with the relative frequency calculator, relative frequency meaning, applications and relative frequency table.

In some cases, it's better to use experimental data instead of theory – and our relative frequency calculator can help you with that. You're probably familiar with the term frequency in statistics, but do you know the relative frequency meaning ? It's not to be confused with frequency in physics!

If the answer is no , read on to find out! We will also show you how to find the relative frequency and use it in the world of sports.

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 quantity computed by the probability calculator that we are so familiar with? Not really; this term is customarily used to refer to 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. You can learn more about it by visiting the coin flip probability calculator !

Such cases are 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.

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 of how many data points share a certain characteristic.

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?

• 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. If you're not sure about the difference between these types, you may want to check the grouped data standard deviation calculator , where it's explored more in-depth.
• 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.
• 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!

Numbers and formulae are hardly ever of any use to 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 :

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.

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:

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

How do I calculate cumulative relative frequency?

Here's how to find cumulative relative frequency:

• 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.
• Add the relative frequencies of previous data points to the relative frequency of the current item.
• 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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• Frequency Distribution | Tables, Types & Examples

Frequency Distribution | Tables, Types & Examples

Published on June 7, 2022 by Shaun Turney . Revised on June 21, 2023.

A frequency distribution describes the number of observations for each possible value of a variable . Frequency distributions are depicted using graphs and frequency tables.

Table of contents

What is a frequency distribution, how to make a frequency table, how to graph a frequency distribution, other interesting articles, frequently asked questions about frequency distributions.

The frequency of a value is the number of times it occurs in a dataset. A frequency distribution is the pattern of frequencies of a variable. It’s the number of times each possible value of a variable occurs in a dataset.

Types of frequency distributions

There are four types of frequency distributions:

• You can use this type of frequency distribution for categorical variables .
• You can use this type of frequency distribution for quantitative variables .
• You can use this type of frequency distribution for any type of variable when you’re more interested in comparing frequencies than the actual number of observations.
• You can use this type of frequency distribution for ordinal or quantitative variables when you want to understand how often observations fall below certain values .

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Frequency distributions are often displayed using frequency tables . A frequency table is an effective way to summarize or organize a dataset. It’s usually composed of two columns:

• The values or class intervals
• Their frequencies

The method for making a frequency table differs between the four types of frequency distributions. You can follow the guides below or use software such as Excel, SPSS, or R to make a frequency table.

How to make an ungrouped frequency table

• For ordinal variables , the values should be ordered from smallest to largest in the table rows.
• For nominal variables , the values can be in any order in the table. You may wish to order them alphabetically or in some other logical order.
• Especially if your dataset is large, it may help to count the frequencies by tallying . Add a third column called “Tally.” As you read the observations, make a tick mark in the appropriate row of the tally column for each observation. Count the tally marks to determine the frequency.

How to make a grouped frequency table

• Calculate the range . Subtract the lowest value in the dataset from the highest.

• Create a table with two columns and as many rows as there are class intervals. Label the first column using the variable name and label the second column “Frequency.” Enter the class intervals in the first column.
• Count the frequencies. The frequencies are the number of observations in each class interval. You can count by tallying if you find it helpful. Enter the frequencies in the second column of the table beside their corresponding class intervals.

Round the class interval width to 10.

The class intervals are 19 ≤ a < 29, 29 ≤ a < 39, 39 ≤ a < 49, 49 ≤ a < 59, and 59 ≤ a < 69.

How to make a relative frequency table

• Create an ungrouped or grouped frequency table .
• Add a third column to the table for the relative frequencies. To calculate the relative frequencies, divide each frequency by the sample size. The sample size is the sum of the frequencies.

How to make a cumulative frequency table

• Create an ungrouped or grouped frequency table for an ordinal or quantitative variable. Cumulative frequencies don’t make sense for nominal variables because the values have no order—one value isn’t more than or less than another value.
• Add a third column to the table for the cumulative frequencies. The cumulative frequency is the number of observations less than or equal to a certain value or class interval. To calculate the relative frequencies, add each frequency to the frequencies in the previous rows.
• Optional: If you want to calculate the cumulative relative frequency , add another column and divide each cumulative frequency by the sample size.

Pie charts, bar charts, and histograms are all ways of graphing frequency distributions. The best choice depends on the type of variable and what you’re trying to communicate.

A pie chart is a graph that shows the relative frequency distribution of a nominal variable .

A pie chart is a circle that’s divided into one slice for each value. The size of the slices shows their relative frequency.

This type of graph can be a good choice when you want to emphasize that one variable is especially frequent or infrequent, or you want to present the overall composition of a variable.

A disadvantage of pie charts is that it’s difficult to see small differences between frequencies. As a result, it’s also not a good option if you want to compare the frequencies of different values.

A bar chart is a graph that shows the frequency or relative frequency distribution of a categorical variable (nominal or ordinal).

The y -axis of the bars shows the frequencies or relative frequencies, and the x -axis shows the values. Each value is represented by a bar, and the length or height of the bar shows the frequency of the value.

A bar chart is a good choice when you want to compare the frequencies of different values. It’s much easier to compare the heights of bars than the angles of pie chart slices.

A histogram is a graph that shows the frequency or relative frequency distribution of a quantitative variable . It looks similar to a bar chart.

The continuous variable is grouped into interval classes , just like a grouped frequency table . The y -axis of the bars shows the frequencies or relative frequencies, and the x -axis shows the interval classes. Each interval class is represented by a bar, and the height of the bar shows the frequency or relative frequency of the interval class.

Although bar charts and histograms are similar, there are important differences:

A histogram is an effective visual summary of several important characteristics of a variable. At a glance, you can see a variable’s central tendency and variability , as well as what probability distribution it appears to follow, such as a normal , Poisson , or uniform distribution.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Student’s t table
• Student’s t distribution
• Quartiles & Quantiles
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

A histogram is an effective way to tell if a frequency distribution appears to have a normal distribution .

Plot a histogram and look at the shape of the bars. If the bars roughly follow a symmetrical bell or hill shape, like the example below, then the distribution is approximately normally distributed.

Categorical variables can be described by a frequency distribution. Quantitative variables can also be described by a frequency distribution, but first they need to be grouped into interval classes .

Probability is the relative frequency over an infinite number of trials.

For example, the probability of a coin landing on heads is .5, meaning that if you flip the coin an infinite number of times, it will land on heads half the time.

Since doing something an infinite number of times is impossible, relative frequency is often used as an estimate of probability. If you flip a coin 1000 times and get 507 heads, the relative frequency, .507, is a good estimate of the probability.

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Turney, S. (2023, June 21). Frequency Distribution | Tables, Types & Examples. Scribbr. Retrieved June 24, 2024, from https://www.scribbr.com/statistics/frequency-distributions/

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