What is Mode?

Dhristi JEE 2022-24

Introduction to Mode

Mode is said to be one of the measures of central tendency to determine the value of a set of data. This value tends to provide a rough idea regarding the items that are present in a data set and the ones that occur most frequently in the set. For example, if there are children who are receiving ice cream from a van that has different flavors involved, the highest number of children who opt for a particular flavor will become the Mode among that data set. 


Mode is considered to be one of the main concepts in Statistics and helps students identify which is the one value that occurs most frequently. Vedantu also explains all about the topic Mode and how these topics will help you learn more about Statistics in general.


In Statistics, Mode or modal value is that observation which occurs at the maximum time or has the highest Frequency in the given set of data. The Mode is derived from the French word La Mode which means fashionable. A given set of data may have one or more than one Mode. A set of numbers with one Mode is unimodal, a set of numbers having two Modes is bimodal, a set of numbers having three Modes is trimodal, and any set of numbers having four or more than four Modes is known as multimodal.


For example, The following table represents the number of runs made by the batsman in the first 10 balls. Find the Mode of the given set of data.

No. of Balls

1

2

3

4

5

6

7

8

9

10

Runs

2

1

1

3

2

3

2

2

4

1


It can be seen that 2 runs are made by the batsman frequently in different balls. Hence, 2 is the Mode of the given data set.


Define Mode

Mode is defined as a value that occurs most frequently in a dataset.


For Example,

In {6, 9, 3, 6, 6, 5, 2, 3}, the Mode is 6 as it occurs most often.


Similar to the Statistical mean and median, Mode is a way of representing important information about random variables or populations in a single number. In a normal Distribution, the value of Mode or modal value is the same as the mean and median whereas the value of Mode in a highly skewed Distribution may be very different.


Mode is the most useful measure of central tendency while observing the categorical data such as the most preferred flavours of soda or Models of bikes for which average median values based on Order cannot be calculated.


Types of Mode

The different types of Mode are Unimodal, Bimodal, Trimodal, and Multimodal. Let us understand each of these Modes.


Unimodal Mode - A set of data with one Mode is known as a Unimodal Mode.


For example, the Mode of data set A = { 14, 15, 16, 17, 15, 18, 15, 19} is 15 as there is only one value repeating itself. Hence, it is a Unimodal data set.


Bimodal Mode - A set of data with two Modes is known as a Bimodal Mode. This means that there are two data values that are having the highest frequencies.


For example, the Mode of data set A = { 8,13,13,14,15,17,17,19} is 13 and 17 because both 13 and 17 are repeating twice in the given set. Hence, it is a Bimodal data set.


Trimodal Mode - A set of data with three Modes is known as a Trimodal Mode. This means that there are three data values that are having the highest frequencies.


For example, the Mode of data set A = {2, 2, 2, 3, 4, 4, 5, 6, 5,4, 7, 5, 8} is 2, 4, and 5 because all the three values are repeating thrice in the given set. Hence, it is a Trimodal data set.


Multimodal Mode - A set of data with four or more than four Modes is known as a Multimodal Mode.


For example, The Mode of data set A = {100, 80, 80, 95, 95, 100, 90, 90,100 ,95 } is 80, 90, 95, and 100 because both all the four values are repeated twice in the given set. Hence, it is a Multimodal data set.


How to Find the Mode?

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


Let us understand how to find the Mode for individual series, discrete series, and continuous series.


Following are the formulas for finding the Mode or modal value for different series.


Individual Series: Simply observe the maximum number of times an individual observation appears.


Let us understand how to find the Mode of individual series with an example:


Calculate the modal value for the following set of data.

12

14

16

18

26

16

20

16

11

12

16

15

20

24


Solution:

Arranging the given set of data in Ascending Order.

11

12

12

14

15

16

16

16

16

18

20

20

24

26


Here, we get 16 four times, 12 and 20 twice each, and other terms only once.


Hence, the Mode for a given set of data is 16.


Discrete Series: Simply find the variables with the highest Frequency incurred.


Let us understand how to find the Mode of discrete series with an example:


A shoe company manufactured winter boots with the size as mentioned below in the Frequency Distribution:

Size of Winter Boots

38

39

40

42

43

44

45

Total Number of Boots

3

1

2

5

4

1

2


Solution:

In the given Frequency Distribution, we can clearly see 42 has the highest Frequency.


Hence, the Mode for the size of winter boots is 42.


Continuous Series: The formula for finding the Mode or modal value in continuous series is given below:


\[ l = f_{1}-f_{0}2f_{1}-f_{2} - f_{0}\times h \]

Where,

l is the lower level of the modal class.

f1 is the Frequency of the modal class.

f2 is the Frequency of class interval succeeding  the modal class.

f0 is the Frequency of class interval preceding the modal class.

h is the width of the class interval.

Let’s understand with an example:

Class Interval

0-5

5 - 10

10 - 15

15 - 20

20-25

Frequency 

5

3

7

2

6


  • Modal Class = 10 - 15 (This is the class with the highest Frequency).

  • Lower level of the modal class (l) = 10

  • Frequency of the modal class (f1) = 7

  • Frequency of class interval succeeding  the modal class (f2) = 2

  • Frequency of class interval preceding the modal class (f0) = 3

  • Width of the class interval (h ) = 5


Finding the Mode

\[ l = f_{1}-f_{0}2f_{1}-f_{2} - f_{0}\times h \]

Mode = 10+(7-3)2(7) - 2- 3 x 5 

= 10 + 49 x 5

= 10 +209

= 10 +2.22

= 12.22

Hence, the modal value for the given Frequency Distribution is 12.22


Solved Examples:

1. Calculate the modal value for the following set of data.

85

86

88

88

91

90

86

92

95


Solutions:

Arranging the data in Ascending Order, we get

85

86

86

88

88

90

91

92

95


As there are two repeating values, it is a bi-modal data.


Hence, the modal values for a given set of data are 86 and 88.


2. Find the Mode for the Frequency Distribution given below:

Age Group of Employees

20 -30

30 - 40

40 - 50

50 - 60

Number of Employees of that Age

30

55

44

25


Solution:

  • Modal Class = 30 - 40 ( This is the class with the highest Frequency).

  • Lower level of the modal class (l) = 30

  • Frequency of the modal class (f1) = 55

  • Frequency of class interval succeeding  the modal class (f2) = 44

  • Frequency of class interval preceding the modal class (f0) = 30

  • Width of the class interval (h ) = 10.


Finding the Mode

\[l = f_1 - f_02f_1-f_2-f_0 \times h \]

Mode = 30+(55-30)2(55)-44-30x10

=30+2536x10

=30+25036

=10+6.944

=36.944

Hence, the modal value for the given Frequency Distribution is 36.944.


Important Points To Remember Regarding Mode:

Below given are some of the important points that will help you summarize the topic and the concept involved in Mode:

  1. Mode value can at times also be the same as mean and /or median however it does not always occur.

  2. Mode is a very useful measure to find out the categorical data

  3. The Mode can also be easily found out for those data sets that do not have any numerical values being involved.

FAQs on What is Mode?

1. What is the Relation between Mean, Median, and Mode in Statistics?

There is an interdependence of all the three measures are the Mean, Median, and Mode. This relationship between all the three measures was provided by Professor Karl Pearson which is an empirical relation. This equation helps a person to find the value of the unknown measure based on the two known measures’ values. The formula to find either of the measures and its values can be provided as follows:


Mean – Mode = 3 (Mean - Median)


Hence using the above formula, it is possible to find out more about the Mode, median, or mean of a particular set of data in Statistics.

2. What if there are two Modes present which Mode will be the answer to the question for the data set provided?

It sometimes happens that there are two Mode values for a given set of data and hence if such a thing occurs then it means that the two values are the most frequently found in a set of data. When such results are obtained then the data set is said to be a bimodal dataset. Such examples occur when there is a large amount of data being grouped. In such cases, due to a random set of data being prepared, there are chances that two of the numbers can be frequented mostly.

3. What if there are no Modes present for the data set provided? How to find a Mode in such a case?

There are chances that a provided dataset has all the numbers that are unique and does not have any number that is repeating. It is during such cases that there is no Mode for the given data set. In such cases, the data set will have no Mode and the Mode is not used as a measure of central tendency. However, there is a formula for finding the Mode by using only the numbers present in the data. All you need to do is take the sum of the two numbers present in the middle and divide by 2. By using this formula you can find Mode for any dataset that does not have Mode present.

4. Why is learning about the topic: What is Mode? 

The topic involve a lot of knowledge with respect to the Statistics and help you find the measure of central tendency. This topic is also one of the main important topics in Class 11 and 12. It is essential that students learn about it. Not only do class tests and semester exams contain questions based on the topic but also competitive exams have a lot of questions being asked based on the topic.

5. Does Vedantu provide any notes or questions on the topic - Mode? 

Vedantu does provide a lot of notes and other resources that help students understand the topic What is Mode? All those students who belong to younger standards can also access these topics and their information as they are not only written in a simple language but also in a way that each and every student can understand well. This will also allow the students of lower standards to prepare for the higher classes and hence help them get more knowledge regarding the topic. Referring to the Vedantu sample papers for the students of Class 11 and 12 will help them understand how to solve questions based on these topics.

6. What are the Advantages of Mode in Mathematics?

Some of the advantages of mode in Mathematics are discussed below:

  • It is simple to understand and easy to calculate.

  • It can easily be calculated for the open end frequency distribution.

  • It is a commonly used technique for calculating average values such as average marks of students, average wages of labours, etc.

  • It can also be found graphically.

  • It can never be affected by extreme values. Hence, it is a good representation of data.

7. What are the Disadvantages of Mode?

Some of the disadvantages of mode are as follows:

  • It cannot be clearly defined in the case of the multimodal series.

  • The value of mode is most affected by the fluctuation in sampling in comparison to the mean and median.

  • Mode is not suitable for statistical analysis and algebraic calculations.

  • Modal value cannot be used to find the total of the whole series as in case of mean.

  • Mode is often determined as ill-defined, ill-definite, and indeterminate.

8. Can the Number 0 be a Mode?

Yes, the number 0 can be a mode if it occurs more than once in a given set of data.

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