Mode in Statistics

Mode

Mode is synonymous with "the most frequent value". When we are asked what the mode is, in fact, we are being asked what is the most frequent number within the total set of numbers.
That is, mode is the number that appears the most times within the set.

How is the mode found?

The number that appears the most times within a set of data is the mode.

How is the frequency of a specific number found?

The number of times a certain number appears within a set is the frequency.

Example

Here is a set of numbers: $4,2,6,4,2,4$
What is the mode?

Solution:
As we have seen, the mode is the number that appears the most times.
In the given set of numbers:
The number $4$ appears $3$ times
The number $2$ appears two times
And the number $6$ appears once.

Therefore, $4$ is the mode.

We can simplify the list to make it easier to identify the mode by grouping like values:

$2,2,4,4,4,6$

Know it's even easier to see that $4$ is the mode.

When using a large set of values, it might be easier to use a frequency table,
for example:

Value	Frequency
2	2
4	3
6	1

Looking at the tables show us clearly which is the most frequent value, in this case, $4$

Mode

In this article, we will learn about the mode, what it is, and how to find it within a table of frequency distribution.
We know it might seem complicated, but we assure you it's a very simple and easy topic.

What is the mode?

Let's look at an example

Here is a set of numbers: $4,15,34,4,15,4$
What is the mode?

Solution:
As we have seen, the mode is the number that appears the most times.
In the given set of numbers:
The number $4$ appears $3$ times
The number $15$ appears two times
And the number $34$ appears once.

Therefore, $4$ is the mode.

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What is frequency?

When we are asked what the frequency of a certain number is, in fact, we are being asked how frequent it is or, in other words, how many times it appears in the set.
Therefore, we have to count the number of times that number appears in the set and this will be the frequency.

Let's look at an example

Here is a set of numbers: $3,3,8,12,3,4,8$
What is the frequency of the number $8$ ?

Solution:
Let's see how many times the number $8$ appears in the set.
The answer is two. Therefore, the frequency of the number $8$ is $2$ .
How is the mode found in the frequency distribution?
In the frequency distribution table, we see all the data neatly organized, showing us how many times each number appears, saving us from counting them on our own.
In the table, we can easily find the mode - it is the number that appears the most times.

Let's look at another example

Here is a frequency distribution table:

Grade	90	80	70	60	50
Number of students	12	13	10	5	6

What is the mode grade (or score)?

Solution:
Great! The frequency distribution table shows us exactly how many students got each grade. The mode is the most common number, in our case the most frequent grade.
In the table, we can see that the grade $80$ has the highest number of students – $13$ , therefore, it can be said that the majority of the students got $80$ .
Thus, the mode is $80$ .

What is the frequency of the grade $60$ ?
Solution:
In fact, we are asked how frequent the grade $60$ is, in other words, how many students received it.
We can find the answer by looking at the table and seeing that $5$ students received $60$ .
Therefore, the frequency of the grade $60$ is $5$ .