Average or mean calculation is one of the most common and basic things in everyday life. If you are a student you will be learning to mean calculation in your second or third grade. Apart from the student's everyone needs to know how to calculate mean, its importance and applications. No matter how much stress is being put on it you never know its real worth!

Importance

If you are conducting a very sensitive experiment and need total precision in it then mean will be your best friend. It happens a lot of times that you get different values after each experiment. The difference between the values is very less and is only some decimal points. The best way to solve these problems is to take the average or means of all the answers. In the end, the result will be considered your significant figure.

This value varies with time and type of experiment. The nature of the experiment will determine the precision of this value. It will increase the significance of your experiment by many folds.

Specific “Means” commonly used in Stats. You’ll probably come across these in your stats class. They have very narrow meanings:

Sampling distribution means:

This is basically used with probability distributions specifically for the Central Limit Theorem. For a set of distributions we call it. Limit of a function is also a very conceptual and important part of math. It comes directly under the subject of calculus, which the students in higher classes study. As it is very conceptual, the calculation of the limit of a function is very intense and one has to take care while calculating it.

Average:

Mean of sample: It is known as the average value in the sample.

Mean of the population: average value in the population

There are a lot of mean types and each of them can be used in the different branches of maths. They are widely used in the finance or physics field. If you are particularly in elementary statics then you will not be able to work without average or mean terms.

What does this mean?

For summarizing a data set we use mean. For the center measurement of any data set, we use mean. It is also exchanged with the word ‘average’. Both have the same meaning.

Formula

Sum of numbers/total number of numbers=average or mean

Following are some of the common types which you will come across in your life:

• Geometric mean
• Arithmetic-Geometric mean
• Root-Mean Square mean
• Heronian mean

The above types are commonly used in statistics specifically when you are studying the population. There are some average points that contribute more than each data point. So there is not any equal distribution of the data points. The arithmetic mean is when all the weights are equal. As shown by Simpson’s Paradox in many instances this mean thing can give incorrect information. It happens in a lot of cases. This concept is used a lot in physics. Problems that include ratios and rates it's better to calculate the average than the arithmetic mean. In fields of computer science, geometry and finance one will find the importance of mean calculation and its implementation.

Geometric Mean

This is the second type of mean. It has a very limited and special role in technology, finance, and social science. E.g you own a stock that's earning 5% the first year, 20% the second year, and 10% the third year. For finding the average return rate you cannot use the arithmetic average. Why? The answer is whenever you are finding return rates you do multiplication, not addition. For example, in the first year, you are multiplying by 1.05.

Arithmetic-Geometric Mean

In machine computation and calculus we use arithmetic-geometric means. (i.e. it's basic for many simple computer calculations). It is basically co-related with the ellipse perimeter. In early times it was developed by Gauss for calculating planetary orbits. This geometric mean is a blend for calculating arithmetic and geometric averages. This is not a surprise. The math behind it is very complicated but one will find a really simple explanation of math here.

Root-Mean Square

This type is very effective in the fields which study sine waves in electrical engineering. This is also known as the quadratic average.

Heronian Mean

This last type of mean is used in the field of geometry for finding pyramidal frustum. This pyramidal frustum is simply a pyramid with its tip sliced off.

Applications

1. A banker needs to calculate mean or average values after every five to ten minutes. Banking is impossible without this term.

2. College students cannot function in any subject without mean calculation apart from languages.

3. Basically, the whole financial and management system works on this specific term. It's a very basic but yet very important term.