To analyse a large group of data, we use statistical tools. Mean median and mode are important statistical tools that are used to interpret the data more precisely. With the help of these statistical measurements, we can categorise the data more easily. Sometimes we need to find the value in the data, which occurs for maximum time in a large group of data. If we start counting everything in a large group of data that will consume lots of time, we use mode to find the value which is the most frequent data. Hence, the mode is one of the important statistical tools which is used in analysing a large group of data.

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Mode

The value or number which occurs maximum time in the data is regarded as mode. In other words, we can say that the most frequently appearing values are known as a mode. If a set of data contains different values or the frequency of each value in the set of data is one, then there is no modal value for that data set.

Types of mode in statistics

Depending upon the number of modal values in the data set, we can divide mode into different types as follows:

Unimodal list- If the set of data consists of only one mode, then the list is regarded as a unimodal list.

Bimodal list – If the data set has two modes, then it is known as a bimodal list.

Trimodal list- The set of data with three-mode is known as a trimodal list.

Multimodal list –If four or more data modal values are present in the list, then it is known as a multimodal list.

Grouped data and ungrouped data

The data in its raw form is the ungrouped data. Here values are placed discretely. Categorising the ungrouped data into a different class on the basis of its characteristics is known as grouped data. The ungrouped data is analysed and categorised to form grouped data.

Mode of ungrouped data

The ungrouped data contains discrete values. To find the mode that is the most frequent value in the data set, we need to arrange the data in ascending order or descending order and then find the frequencies of each value. The value which has maximum frequency will be the mode of ungrouped data.

For example, consider the data – 4,6,3,10,4,8,9,3,6,7,3,5,3,2,9

Arranging the data in ascending order 2,3,3,3,3,4,4,5,6,6,7,8,9,9,10

Since the value 3 is repeated four times; hence the mode of the given data is 3

Mode of grouped data

In grouped data, we categorise the data into different classes. A class interval is formed for each class, and each data value’s frequency is distributed accordingly. To calculate the mode of grouped data, we have the following formula

Mode = L + (f1-  f02f1-  f0-   f2 ) h

Here h Is the size of class interval

L is the lower limit of the class interval of modal class

f1  is the modal class frequency

f0 is the preceding class frequency

f2 is the succeeding class frequency

Steps to find a mode of grouped data

Step 1 – First, we will identify the modal class. Modal class is the class that has the highest frequency.

Step 3 – Then, we will find the value of h, which is the size of the class interval, and can be calculated by using the formula, upper limit – lower limit.

Step 2 – With the help of the modal class, we will find the values of f0, f1,f2.

Step3- From the class interval corresponding to the modal class, we will find the value of the lower limit, L.

Let us take an example to understand how to calculate the frequency of grouped data.

Class Interval	Frequency(No of students)
0-10	2
10-20	4
20-30	8
30-40	5
40-50	6
Total	25

The above table represents the marks obtained by 25 students in mathematics examination

The class interval 20-30 has the highest frequency 8, thus the modal class is 20-30

From the modal class we have, L= 20  , f1 = 8 , f0 = 4 and f2 = 5

h = upper limit – lower limit

=>  h = 10

Putting these values in the formula,  Mode = L + (f1-  f02f1-  f0-   f2 ) h

We will get, mode = 20 +( 8-42X 8-4-5  ) x 10

Mode = 20 + 47 x 10 =   25.71

Conclusion

In this article, we have learnt about the mode, which is the statistical tool that helps us find the most repeated value easily. The mode is the value that occurs most frequently in the data set. The list of data is further divided into types of a modal list like unimodal, bimodal, trimodal, and multimodal. The mode of ungrouped data can be found easily by finding the value with maximum frequency whereas the mode of grouped data can be found by the formula.

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