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Bhangra’s is a very popular shop that sells watches of foreign brands in Delhi’s posh Connaught Place market. The owner of the shop decided to stock the brand whose watches were selling the most. He decided to look at the previous month’s sales, which is listed as

Brand

Number of watches sold

Alpha

17

Townzen

23

Tag Heuim

7

Twatch

13

Based on this information, the owner decided to stop keeping Tag Heuim watches because very few people buy them. He also decided to keep more varieties of Townzen watches because most people were buying this brand.

In this data set, the highest occurring event (23) corresponds to Townzen watches and is known as the mode of this data set. Just like mean and range, mode is another measure of central tendency of a group of data. It can be defined as

The value of a set of data that occurs most often is called the mode of the data.

Let us find the mode of another data set in the given video.

Here, the data set did not contain too many terms and could thus be easily arranged in ascending order. However, in case of very large data, it is not always easy to arrange it in ascending or descending order. Therefore, in such cases, it is better to arrange the data set in the form of a table with tally marks.

So let us understand the usage of tally marks method to find the mode with the help of the given video.

A collection of data can have more than one mode. The data sets having one mode or two modes or more than 2 modes are  said to have uni-mode or bi-mode or multi-mode

Let us now look at some more examples to understand this concept better.

Example 1:

Find the mode of the following numbers.

2, 6, 7, 5, 4, 2, 6, 7, 9, 7, 8, 3, 2, 11

Solution:

The given set of numbers can be arranged in ascending order as

2, 2, 2, 3, 4, 5, 6, 6, 7, 7, 7, 8, 9, 11

Here, 7 and 2 occur most often (3 times). Therefore, both 7 and 2 are the modes of the given set of numbers.

Example 2:

Find the mode of the following data set.

1000, 200, 700, 500, 600, 160, 270, 300, 360, 950

Solution:

The increasing order of the given numbers is

160, 200, 270, 300, 360, 500, 600, 700, 950, 1000

Here, every number is occurring only once.

Thus, the given data has no mode.

Note: The above example shows that the mode of a data may or may not be unique. Also, there are some data sets which do not have any mode.

Example 3:

Determine whether the data 35, 30,  32,  35,  40,  30,  25,  30,  22,  30 has uni-mode, bi-mode or multi-mode.

Solution:

From the data, we observe that 30 repeats maximum times (4 times). Thus, the mode of this data is 30. Since there is only one mode of this data, so the given data has uni-mode.

 

Example 4:

Find the type of mode of the data 25,  23,  23,  25,  27,  26,  23,  24,  23,  25,  28,  25.

Solution:

From the data, we observe that 23 and 25 repeats maximum times (4 times). Thus, the mode of this data is 23 and 25. Since there are two modes of this data, so this data has bi-mode.

 

Example 5:

Which type of mode is represented by the data as shown below?

Solution:

From the frequency table, we observe that 16, 24 and 32 repeats maximum times (9 times). Thus, the mode of this data is 16, 24, and 32. Since there are three modes of this data, so this data has multi-mode.

Application of Mean in Real Life

The runs scored by the two opening batsmen of a team in ten successive matches of a cricket series are listed in the table.

Player A 24 50 34 24 20 96 105 50 13 27
Player B 26 22 30 10 42 98 40 54 10 122

Using this data, we can compare the performances of the players for each individual game. For example, pl...

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