In some cases, it's better to use the 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.

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 result Relative frequency
Win
5/11
Draw
2/11
Loss
4/11

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.

Madhu Raman and Michael Darcy
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