# Mode Calculator

Created by Hanna Pamuła, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Feb 01, 2023

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 the 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 gentlemen, 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 obtained with this calculator is one of many ways to measure the center of a dataset. Along with this one, you can come across other central tendency calculators, such as:

• Mean calculator: it calculates the mean (also called average) by summing up all of the numbers and dividing it by the number of numbers;
• Median calculator: it finds the median, which is the middle number in the ordered dataset; and
• Range calculator: finds the difference between the largest and smallest value of the set, which is the range.

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 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 it 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:

Value

Number of occurrences

12

1

15

2

17

2

22

1

23

2

24

1

26

3

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.😎

🔎 You can also visualize the data using a stem and leaf plot calculator to figure out the range in which most of your values lie.

Up to now, we only showed you 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, we say its distribution is 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 rocket science🚀, really, but just in case, here are the detailed instructions:

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.
Hanna Pamuła, PhD
Dataset (You may enter up to 50 numbers)
x₁
x₂
Step by step solution
None
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