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# Mode Calculator

By Hanna Pamuła, PhD candidate

Welcome to the mode calculator - a tool that lets you find the mode of a set in two shakes of a lamb's tail. Input your numerical dataset and we'll show you the modal value, as well as instructions on how to calculate mode. However, if you're uncertain what the mode in math is, don't worry too much - we'll solve this problem for you too. Read through our simple mode definition with an explanation, and everything should be as plain as day! 🌞

## What is a mode in math? Mode definition

Searching for the mode definition, also called the modal value? Well, ladies and gentleman, here it is:

 💡The mode is the value that appears most often in a given dataset.

For example, if your dataset consists of five elements: {3,5,7,3,3}, then the mode of this set is 3. Wasn't that easy? 😉

The mode is one of many ways to measure the center of a dataset. Along with mode, you can come across terms such as:

• Mean, which is also called average, is calculated by summing up all of the numbers and dividing it by the number of numbers;
• Median, which is the middle number in the ordered dataset; and
• Range, the difference between the largest and smallest value of the set.

One more thing worth mentioning is that, contrary to the median and mean, our dataset doesn't need to be numerical to find the mode. Have a look at these two examples:

1. You have a bag of fruits: 🍊🥝🥝🍋🍌🍌🍏🍓🥝. We can define the mode as the fruit that occurs most often in your set - so the kiwi fruits🥝. The modal value is the only measure of central tendencies we can determine - finding the median or mean of a bag of fruits is impossible. 🤷

2. Your five closest friends' names are Emma, Mia, Marie, Emma, and Olivia. What's the mode - the most popular name in your bunch of friends? It's Emma, of course. We can't imagine taking the average of your friends' names 😂

However, in the vast majority of cases you'll deal with numbers.

## Easy methods to remember what the modal value is

Do you sometimes feel that you have a mind like a sieve🤯, and all these math terms will quickly disappear? We have a solution for that - use one of the mnemonics techniques to remember forever what a mode is in math.

• The word MOde is a bit similar to the word MOst - and mode is the most common value;
• You can also associate mode with the old fashioned term a la mode, meaning something fashionable or trendy (and thus happening often in the population); and
• Another option is learning an alternative version of the nursery rhyme Hey Diddle Diddle by heart. This time the cow's not jumping over the moon 🐄🌙, but you sing about the measures of central tendency:

Hey diddle diddle,

the median's the middle,

you add and divide for the mean;

The mode is the one

that appears the most,

And the range is the difference between.

Choose your favorite mnemonics technique to never fret about forgetting the mode definition again💪

## How to calculate mode? How to find the mode of a data set?

Let's assume that you have a set of numbers A = {17, 23, 26, 12, 23, 22, 15, 26, 15, 24, 26, 17}. How to calculate the mode of such a dataset?

It's not a necessary step, but may be helpful - especially if your dataset is quite big. Arrange your numbers in order:

A = {12, 15, 15, 17, 17, 22, 23, 23, 24, 26, 26, 26}

2. Pick the number that appears most often - that's the mode

A = {12, 15, 15, 17, 17, 22, 23, 23, 24, 26, 26, 26}

For our dataset, the mode is 26.

3. To present the result in a more explicit form, you may create a frequency table:

ValueNumber
of occurences
121
152
172
221
232
241
263

Another method to find the mode is by ticking the marks on a number line - that's a way of dealing with the mode if your dataset is not too large and the numbers are not dispersed.

And last, but not least, you can use our mode calculator.😎

Up to now, we only showed you the examples where exactly one number occurs more often than the others. But what happens if the mode is not unique? This could mean that, e.g., two elements appear in the dataset the same number of times? Well, it's possible - in such cases, all the variables with the most occurrences will be a mode of the dataset:

• If the dataset has more than one mode, you may call the distribution multimodal, e.g. C = {1,1,4,6,6,7,7,8,9}, with modes 1,6 and 7.
• The dataset B = {6,2,4,4,7,6} has two modes - 4 and 6. We may say that the dataset is bimodal

But, if all numbers occur the same number of times, then there's no mode.

## How to use the mode calculator: an example

If you are still wondering how to find the mode of a data set, just use our mode calculator. How do you do that? Well, it's not a rocket science🚀, really, but just in case here's the detailed instruction:

1. Input your numerical data into fields. You don't need to put them in order, you can just enter the data as it is. New boxes will appear as you need them.
2. The modal value will appear instantly - you'll find it directly under the data.
3. You can also choose a step-by-step solution, either a frequency table or the sorting method.

If you want to practice your newly gained knowledge, check out the real-life scenario we've created: A streamer's road to fame. In this word problem, you'll deal with mode and other descriptive statistics, such as variance and standard deviation.

Hanna Pamuła, PhD candidate