What Is Modal In Maths? A Detail Explanation Of Mode, Modal, And Mean

Functional Skills

Ever sat in maths class wondering what is modal in maths while your teacher rambled on about numbers? You’re not alone. I am a tutor, a mother, and a former student. I can confirm that I’ve seen people get scared with a question on how to calculate the modal value.
When we hear about modal, we get confused, and when we hear about the other three M-words, that is Mean, Median and Mode, confusion just doubles up.
So, here I’ve brought a new and the best way of learning that will not just help you understand what a modal, mean, and median are in mathematics but also help you remember them with some quick tips.
So what are we waiting for? Let’s start and make these confusing terms more understandable in the easiest way possible.

What is Modal in Maths? The Easiest Way

In maths, the modal value or mode is simply the number that appears most frequently in a dataset. For example, if you’ve got a collection of numbers like 3, 7, 5, 3, 7, 8, 7, 9. Then 7 is your mode because it shows up three times, while other numbers appear only once or twice.

The beauty of the mode is its straightforwardness. Unlike the mean or median, which require formulas and calculations, finding the mode just needs you to count occurrences. It’s especially useful when dealing with categorical data where averaging doesn’t make sense.

Note: Modal = Mode = Number Repeated Highest Times in the Data Set

What is Modal Value? Real Life Example

As explained, the modal value, which is also known as the mode in statistics, is the value that appears most frequently in a set of data. It also represents the most common number/observation within a dataset. The best way to understand the modal value is with a real-life example.
Example: Think about your favourite coffee shop. They might track which drinks people order most often. If 45 people order lattes, 28 order cappuccinos, and 17 order flat whites, then the latte is the modal choice. The coffee shop owner might use this information to stock more milk or train more baristas on latte art.

Now you know how you see the popular choice or the best-selling products on the e-commerce websites. Well done!

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Our Level 1 Functional Skills Maths course is designed to help learners develop essential mathematical skills for everyday life, work, and further study. This course covers key mathematical concepts such as numbers, fractions, decimals, percentages, ratios, and problem-solving strategies. It also explains how to apply maths in real-life situations, including budgeting, measuring, and interpreting data.

The mode gives us insight into popularity or common occurrences. It answers questions like:

Which shoe size sells most frequently?
What colour car do most people choose?
Which answer did students select most often on a multiple-choice question?

So, if you see questions like this in the paper, you know what you’d have to calculate!

How to Find the Modal Value in a Dataset

To find the modal value, first count the frequencies and then look for the number that appears the most frequently. To keep it easier, you can follow these three steps:

Step 1. Organise your data (optional but helpful)
Step 2. Count how many times each value appears
Steps 3. The value with the highest frequency is your mode

Let’s see this with a simple example. Imagine you’ve surveyed 15 people about how many pets they own:

0, 2, 1, 0, 3, 1, 2, 1, 1, 0, 2, 1, 0, 1, 2

0 appears 4 times
1 appears 6 times
2 appears 4 times
3 appears 1 time

The number 1 appears most frequently (6 times), so 1 is the modal number of pets owned.

What If There’s More Than One Mode?

Now here comes the biggest and most common question. What if there’s more than one mode in the dataset? Sometimes you’ll encounter datasets with multiple modal values. When two or more values share the highest frequency, we call the dataset bimodal or multimodal.

For example, in the data set:

4, 7, 2, 7, 4, 9, 4, 7, 5, 8

Both 4 and 7 appear three times each, while other values appear only once or twice.

Here, the answer is that this dataset is bimodal with modes of 4 and 7.

When a dataset has multiple modes, all the numbers or values with the highest frequencies will become the modal value. This can actually provide deeper insights since it might indicate different groups within your data.

No Mode? It’s Possible!

Yes, sometimes a dataset has no mode at all. If every value appears exactly the same number of times, there’s no single most frequent value.

For instance, in the dataset:

5, 8, 12, 15, 20

Each number appears exactly once, so there’s no mode. Mathematicians would describe this dataset as having “no mode” or sometimes as “all values are modal.”

The Modal Class in Grouped Data

The modal class is simply the group containing the most data points. It’s particularly useful when dealing with continuous data that’s been categorised into intervals. When working with larger datasets, data is often organised into groups or classes. For instance, test scores might be grouped as 0-10, 11-20, 21-30, and so on.

Score Range	0-10	11-20	21-30	31-40	41-50
Frequency (Number of Students)	2	5	8	10	5

How to Identify the Modal Class

Let’s say you’ve collected the following test scores for 30 students:

The modal class here is 31-40 because it contains the highest number of students (10).

Types of Mode in Mathematics

There are several types of modes for calculating the most frequent number. The common modes are unimodal,bimodal, trimodal and multimodal.

Unimodal or One Mode

If one number shows more than the others, it is called the unimodal.It is the simplest way to find the common values in the dataset. For example, you have the set of values: 4, 3, 5, 6, 7, 2, 4. Here, the number 4 appears 3 times, which is more than the other numbers. So, the mode is 4.

Bimodal or Two Modes

If any number appears two times in the data set, it is bimodal. For example, the set of numbers is 3, 1, 5, 3, 9, 5. According to this, 3 and 5 appear twice. So, here the bi-modal values are 3 and 5.

Trimodal or Three Modes

When the numbers occur three times, it is called trimodal. For example, the set of numbers is 9, 2, 5, 9, 8, 9, 5, 2, 5, 9. In this data set, 9 appears 4 times, 5 appears 3 times, and 2 appears 2 times. The trimodal values are 2, 5, and 9.

Multimodal or More Than Once

If the numbers appear more than once, it is multimodal. For instance, the number set is- 4, 2, 4, 2, 5, 6, 5, 1, 6, 4, 6, 4, 3, 5. Here, the frequent numbers are 2, 4, 5, 6. So, the multimodal values are 2, 4, 5, and 6.

Difference Between Mean, Median and Mode

The mean, mode, and median are examples of descriptive statistics. Here, the mean, median, and mode are statistical averages that show the central value. Both are different, but they help us to understand the data distribution in statistical analysis.

Below you’ll see the mean, median and mode explained with an example in the most structured manner. Questions similar to these are multiple times asked in the Functional Skills Maths Level 2 and Maths GCSE exams. This section will help you prepare for both. This will resolve all the confusion and make you remember it for a long go! No boring explanations, just what you need to know!

What is a Mean?

Mean is the average of the numbers given in the dataset. You find the mean by adding all the numbers together and then dividing by how many numbers there are.

Formula: Mean = Sum of all the values ÷ Total number of values

How to Calculate the Mean in Maths

Add up all the numbers
Divide the total by how many numbers there are

Example:
Numbers = 4, 6, 8, 10
Total = 4 + 6 + 8 + 10 = 28
How many numbers? = 4
Mean = 28 ÷ 4 = 7

What is a Median?

The median is the middle number in a sorted list of numbers. To find a median you have to put the numbers in order. If there is one middle number, that’s the median. If there are two middle numbers, find their average.

Formula

Odd number of values: Median = Middle number

Even number of values: Median = Middle two numbers added together ÷ 2

How How to Calculate the Mean in Maths

Put the numbers in order (smallest to biggest)
Find the middle number
If there’s an even amount of numbers, take the mean of the two middle numbers

Example to calculate median of an odd data set
Numbers = 3, 5, 8
Median = 5 (middle one)

Example to calculate median of an even data set
Numbers = 2, 4, 6, 8
Middle two = 4 and 6
→ (4 + 6) ÷ 2 = 5
Median = 5

What is a Mode?

As already explained, the mode is the number that appears most often in a set of numbers. Here you only have to look for the number that repeats the most. There can be one mode, more than one, or none at all.

Formula

There’s no formula, just find the value(s) that appear most frequently. Easy!

How to Calculate the Mean in Maths

Look at the numbers in your list
Find which number(s) appear most often

Example:
Numbers = 1, 2, 2, 3, 4, 4, 4, 5
Mode = 4 (it appears 3 times)

Practical Examples of Mean, Median and Mode

Let’s make this concrete with some examples that we have came across in the GCSEs or Functional Skills Exams.

Example 1: Classroom Test Scores

Consider these test scores: 65, 70, 70, 75, 80, 85, 90

Mean: (65 + 70 + 70 + 75 + 80 + 85 + 90) ÷ 7 = 535 ÷ 7 = 76.4
Median: 75 (the middle value when arranged in order)
Mode: 70 (appears twice, more than any other score)

What does this tell us? The average score (mean) is 76.4, but the most common score (mode) is 70. The middle score (median) is 75.

Example 2: Monthly Salaries in a Small Company

Consider these monthly salaries: £1,500, £1,600, £1,700, £1,800, £1,900, £2,000, £10,000

Mean: (£1,500 + £1,600 + £1,700 + £1,800 + £1,900 + £2,000 + £10,000) ÷ 7 = £20,500 ÷ 7 = £2,929
Median: £1,800 (the middle value)
Mode: None (no value appears more than once)

See how the mean is much higher than most salaries? That’s because it’s pulled up by the £10,000 outlier. The median gives a more realistic picture of what a typical employee earns.

Common Errors and How to Avoid Them

Watch out for these common mistakes:

For Mean:

Forgetting to account for frequency (when values repeat)
Including text or non-numeric values in calculations
Using the wrong average type for your situation

For Median:

Not ordering the data first
Miscounting positions for the middle value
Forgetting to average the two middle values for even-sized datasets

For Mode:

Assuming there’s only one mode
Reporting a mode when no value repeats
Using mode for continuous data without grouping

Conclusion

Great job! Now you know what exactly is modal in maths, and in addition to it, you have also learned about mean, median and mode. So, the next time you come across the question of how to calculate any of these averages, I hope you won’t feel the panic that so many of us once did. So, as I said, with the right explanation and a few simple tricks, they really do start to make sense. I created this blog to break down the confusion and help you remember the differences in the easiest way possible. Keep practising what you’ve learned here and soon, these maths basics will feel like second nature.

FAQs

Can a Data Set Have No Mode?

Yes. If a data set has no frequent numbers or no number appears more than once, it is considered to have no mode. It is also called an amodal data set. In that case, it won’t be used as the central tendency in statistics. For example, you have a data set of 2, 5, 7, 9, 11, 14. Here, all numbers are used only once, so it’s a no-mode data set.

Can the Mode be Used for Qualitative Data?

Yes. You can use mode for the qualitative data because it identifies the most frequently occurring category. It helps to find the common value, name, or number in a grouped and individual data set. Mode can be used for collecting different types of surveys to find the most popular opinion or data.

Is the Mode Used in Statistics?

Yes. The mode is used in statistics to measure central tendencies in data analysis and management, along with the mean and median. It helps to understand the most occurring value of qualitative and quantitative data types.

What is the Modal Value in Real Life?

The modal value in real life is assessing the common numbers, trends, or patterns. It is used in retail, educational institutions, manufacturing industries, regular surveys, data management, and market research.

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