What is mode in math?

Mode is a level of frequency that is most common in a set of data and for which there is no other level that is more common and closer to the average. Again, people use mode to represent the most frequent number in a set of data.

For example, in the set {(2,4),(3,6), (2,5)} of data, the most common number is 2 and there is no other number that is more common and closer to the average.
In this case, it is said that the mode of the set is 2.

In simple mode represents a data set with one most frequent number and no other more frequent number closer to the average. But it can be more than one mode in a data set too.

The number appears most often in a set of numbers.
​Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often).

Mode is the term given to the value that appears the most often in a set-off number. For example, if the ages of students in a class is [14,14,15,15,15,15,15,15,16,16,16,17,17] the mode is 15 as it shows up 6 times, more than any of the other ages.

The formula of Mode.

Mode = L + (fm−f1)h /2fm−f1−f2

Where

L = lower limit of the modal class,

h = size of the class interval (assuming all class sizes to be equal),

f₁ = frequency of the modal class,

fo= frequency of the class preceding the modal class,

f2 = frequency of the class succeeding the modal class.

Advantages of Using Mode

In certain cases, the mode can be an extremely helpful measure of central tendency. One of its biggest advantages is that it can be applied to any type of data, whereas both the mean and median cannot be calculated for nominal data. It is also not affected by extreme values in datasets with quantitative data. Thus, it can provide insights into almost any dataset despite the data distribution.

On the other hand, the statistical measure also comes with its own limitations. For instance, it cannot be further treated mathematically. Therefore, the measure cannot be used for more detailed analysis. In addition, since it is not based on all values in the dataset, it is difficult to draw conclusions regarding the dataset relying on mode only.

How To Use Mode?

Let's understand the mode using a simple example

3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

In order these numbers are:

3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56

This makes it easy to see which numbers appear most often.

In this case, the mode is 23.

More Than One Mode
We can have more than one mode.

Example: {1, 3, 3, 3, 4, 4, 6, 6, 6, 9}
3 appears three times, as does 6.

So there are two modes: at 3 and 6

Having two modes is called "bimodal".

Having more than two modes is called "multimodal".

Conclusion

A measure of central tendency is a measure that tells us where the middle of a bunch of data lies.

   The three most common measures of central tendency are the mean, the median, and the mode.

1. Mean: Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average.

2. Median: Median is the number present in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers.

3. Mode: Mode is the value that occurs most frequently in a set of data.

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