 ## Mean – What? How? Benefits? Limitation?

Mean in simple terms is defined as an average value attained. Whenever the word is used without a modifier, it is assumed to be arithmetic mean. Simple or arithmetic mean of a range of values or quantities is computed by dividing the total of all values by the number of values. It is the most common and best general-purpose measure of the mid-point for a set of values.

## How Do We Find Mean?

Let’s try to understand this using the marks scored in mathematics by 6 six students in class 5

 Student Marks Obtained (Out of 20) Student A 3 Student B 5 Student C 7 Student D 7 Student E 17 Student F 15

Step 1: Collate the marks of students: 3, 5, 7, 7, 17, and 15.

Step 2: We will first add marks of all the students: 3 + 5 + 7 + 7 + 17 = 54

Step 3: The total number of students are: 6.

Step 4: Dividing the sum of all marks by the total number of students: 54/6

Step 5: Mean: 9

In the above example, we found that the mean marks scored in maths for six students in a class is 9. It can be noticed here that two students (Student E and F) are performing above average and the rest of the students are having a below average performance in the class. Mean helps us to find the central tendency or the center point of values in a range which helps us to understand the relative performance in the range of values.

## Benefits Of Mean

One of the most widely used concept is not because of nothing. Mean comes with a host of benefits:

• It helps us to understand our population in a better way. For example, during resource allocation of a certain task, the manager can try to understand the mean time required for a certain task and accordingly he can use that value to plan the workload for his team. To understand this point further, we can take the example of a manager who wants to allocate some standard reports in pipeline to his team members. He will first calculate the mean time required to finish a report and then will calculate the time availability of his resources. Now using these two data, it becomes very easy for the manager to plan the work which he has received with his team.
• Whenever we do not have a lot of time to analyze our data or we need a quick read of the results. We look at the mean to see where exactly are the values falling around.
• Mean is not only quick but also very easy to calculate. Be it excel or R or Python, finding mean is very easy.

## Limitation Of Mean

Even though mean is one of the widely used concepts, it comes with its own set of limitation

• Whenever we have an extreme value or an outlier, the mean score of a set of values is corrupted. To address this problem, we use other concepts in statistics like median, mode, etc which have less impact because of outliers. An example to this limitation would be taking the score of students in a mathematics test, say students have received 18,16,15,14 and then 3. Here the mean score would be 13.2. However, it is not the central tendency of our dataset. This is because there is an outlier score of 3 in our dataset which has impacted our mean to pull it down significantly.
• Sometimes mean does not coincide with any of the values present in our set. For example, if we take the average children in each family. We might get the mean value to be something like 2.3. However, it is not humanly possible to have 2.3 kids to anyone.
• It cannot average percentage and ratios properly.

## Types Of Means

There are various types of means and though in our post we have primarily covered arithmetic mean we will over the period of time look into each type of mean and its application. The various types of means which we will look into are:

• Pythagorean mean
• Arithmetic mean
• Geometric mean
• Harmonic mean
• Power mean or holder mean
• F-mean
• Weighted arithmetic mean
• Truncated mean
• Interquartile mean
• Mean of a function
• Mean of angles and cyclical quantities
• Frechet mean
• Arithmetic-geometric mean
• Arithmetic-harmonic mean
• Cesàro mean
• Chisini mean
• Contraharmonic mean
• Elementary symmetric mean
• Geometric-harmonic mean
• Grand mean
• Heinz mean
• Heronian mean
• Identric mean
• Lehmer mean
• Logarithmic mean
• Moving average
• Neuman–Sándor mean
• Root mean square (quadratic mean)
• Rényi’s entropy (a generalized f-mean)
• Spherical mean
• Stolarsky mean
• Weighted geometric mean
• Weighted harmonic mean