In the context of the particular discussion, there is no doubt that there is a perfect definition of average. Normally, average refers to the arithmetic mean, and with the help of the letter “A”, this part of mathematics is denoted. Conversely, it can be stated that the main role of arithmetic mean or average is to identify the central tendency. Therefore, it is clear that the average is defined as the number which is calculated by the entire quantities and then divided by the total by the number of quantities. Therefore, it is clear that average is very essential.  

Discussion 

Properties of average function

There are some essential properties of average function because it is a crucial part of mathematics and also statistics. These properties are discussed below:

1. One of the relevant properties of average is that it can lie between the maximum and the minimum observations. 
2. It can be stated that the average is simple and easy to calculate the numbers and identify the central tendency. 
3. The other feature of average is that it can be properly defined as well as described by the particular mathematical formulas. 
4. The extreme values cannot affect the average and for this reason, it is considered as the property or feature of average. 

Types of average function

There are some important types of average such as mean, median, mode, range. These types are discussed below:

Definition of mean: In the context of the discussion, it can be stated that mean is the most essential concept of average related to statistics and mathematics. Basically, it is the type of mathematical average that comprises two or more numbers. It can be also stated that summing the number of sets and dividing by the total number provides the result of the arithmetic mean.  

Definition of median: It can be stated that the median is also considered as a particular part or concept of mathematics and statics. In the context of mathematics, the median refers to the middle value of the sorted list of numbers. On the other hand, it can be also stated that, in the case of two middle numbers, one must take the mean of those particular numbers. 

Definition of mode: the other effective concept of average is the mode which is also important in mathematics as well as statistics. Mode is considered as the most essential and frequent number which is defined as the number that occurs the highest number of times. It can be stated that mode has three main types.  

Example of average function

In the context of the particular study, there are some examples of average function which are considered as the example of mean, median, and mode. These examples are given below:

Example of mean: The example of the mean is given below:

Mean of 4,1 and 7 is (4+1+7)/3=12/3=4

Example of median: the example of the median is given below:

Median of 5, 3, 12

Put the number in this particular order 3, 5, 12 and the middle value is considered as 5. 

Example of mode: There is the example of mode also which is given below: 

First, find the mode class and then find the size of the modal class and then find the value of mode with the help of the formula. There are three types of modes such as unimodal class, bimodal classroom, trimodal class, and multimodal class. 

The formula of average function

These formulas are related to the average functions which are discussed below:

The formula of mean: The formula of arithmetic mean is m= {sum of the terms} ÷ {total number of the terms}

Formula of median: The formula of median is median (x)={(n+1)/2} for the odd numbers. In the context of even numbers, the formula is median(x)= {{(n/2)} +{(n/2) +1}}/{2}. 

Formula of Mode: the formula of mode is L+(fm-f1) *h/(fm-f1) +(fm-f2).

Conclusion 

In the context of the study, it can be concluded that the average has different uses in the practical life of people. All the medical study is based on the average as well as statistics.  On the other hand, it can be stated that this part of mathematics also helps to monitor the mental and physical development of a child. In other words, there is no doubt that apart from the mean, the other two types of average are median and mode which are also essential to calculate the numbers. The average is significant in the study of mathematics because it is representative of entire data and information. In other words, it can be stated that the three types of average such as mean, median, and mode are equally important in statistics.