Shankar D.K — June 18, 2021

This article was published as a part of the Data Science Blogathon

## Introduction

Imagine you run a startup and you decide to share 10% of your excess profit with all your employees as a festive bonus. You have various stages of workers from low level to higher. But you don’t want to be biased. So you make a decision of giving an equal amount of bonus to all your employees irrespective of their positions. Now you have confusion on how to fix that amount, because if you fix it randomly it may cause loss for you. In that situation what can you do?

Answer: List the 10% salary of all stages of your employee and take an average. Then give that average amount to all your employees as a festive bonus. This is the finest solution for your confusion.

### Ok now think what this Average is? Image Source

The common analytical terminology among the common people is “Average”. The names of calling this may be different but the term is one and the same. Even though people aware of this, more than 90% of them thinking that the Average is simply mean and median. But in reality how many of you know that the apart from the above two Average has many classifications?

### Definition of Average:

The representation of a whole set of data in a single value is known as Average. Generally, this tends to be the calculated central value of the distribution. This is the reason why it is called the Measure of Central tendency. Or in other words, it represents the appropriate position of the data set so this is also called the Measure of Location.

### How to find an ideal average: Image Source

To find a good average, make sure that the average must meet the desired characteristics

• It should not be affected by extreme values
• It should be simple and easy to calculate
• It should be capable of further Statistical treatments
• It should be clear and stable
• It should not be affected by skewness

### Types of Averages:

The Major Classifications of averages in Statistics are

1. Mathematical Averages
2. Positional Averages
3. Commercial Averages Image Source

## Mathematical Averages:

The Mathematical Averages are also called Arithmetic Averages. It is the kind of simple average and it has the capability of handling the  Quantitative data effectively.

The types of Mathematical Averages are:

· Arithmetic Mean

· Geometric Mean

· Harmonic Mean

The most popular type of average is calculated by taking the sum of the group of values and dividing it by the number of values of the respective set, which is most commonly known as Arithmetic Mean. Image Source

But in the case of geometric and harmonic means, the values are calculated using the product and reciprocal of the values rather than taking the sum.

Example: Take 18,22,26,34,39 and 41. Find their average?

Let the sum of their heights be 180

Now divide it by the total number be 180/6= 30

The average value be 30

## Positional Averages:

The positional Averages are the type of averages whose value is defined by its position of which it represents the whole set of samples. This is an effective measure for handling nominal kinds of data.

While in the case of mathematical averages the calculated value might not be in the series of the respective data set but in the case of positional averages, the calculated average value must be a value that lies within the set of observed data.

The types of Positional Averages are:

· Median

· Mode

· Quantiles (Quartiles, Quintiles, Octiles, Deciles, Percentiles) Image Source

Example: The respective heights of the 5 brothers be in cms 150,151,149, 155,145. Find their average height?

Lets arrange the values in ascending/descending order: 145,149,150,151,155

Now mark the Centre value =150

The average height of those brothers be 150 cm

Commercial Averages:

These are the types of averages that fix a number and find a prospective set of series of averages. These are commonly used by commercial institutions to find their profit and loss.

In spite of being a single value like other types of averages, these are mostly a series of values.

The types of Commercial Averages are:

· Moving Average

· Progressive Average

· Composite Average

This kind of averages is mostly used in the commercial sectors to understand the trend analysis, business forecastings, etc. Image Source

Example: The last 5 closing stock values of the reliance industries are given 323,343,319,325,349. Find its two-day moving averages?

Calculating Measure of  Moving Average: (a+b)/2, (b+c)/2, (c+d)/2, (d+e)/2

The resultant Moving Averages be:             333,           321,      322,    337

With these values, a trend line is drawn to find the prospective or retrospective trend of the stocks

### How to differentiate the types?

#### · Mathematical Averages:

These are the kind of Averages which can be used when the data is quantitative and continuous in nature. The resultant must be fall between the ranges of the dataset. It is used in the critical mathematical computations

Example: Blood Pressure Average of the patients,  Average rainwater received in a particular period ·Image Source

Positional Averages:

In this type, the data should be discrete data and most probably a nominal kind. The output value must lie within the set of data. In some of its types, the input values have repetitions, lies within some particular ranges, most probably it should be in absolute numbers.

Example:  Average weights/Heights, Age-wise vaccinated average

· Commercial Averages:

These are the averages whose output should not be a single value like other types. The Commercial Averages produce series of output values to create trends of the given data. They are mostly used in the commercial sectors to analyze the exponential growth of the business.

Example: Share market trend flow, Business profit/loss exponential trend. Image Source

Conclusion

Since the Measures of Averages are the most important and popular method of analysis. It is the most simple and effective measure for getting appropriate results. But before using this method “There is always a clear and basic understanding is needed for how to use and where to use the respective types of averages for to get better output with maximum accuracy”. 