Mean

Introduction

In our day-to-day lives, we use mean. When a certain data is required to give a brief idea of the overall data, the mean is usually applied. For instance, when watching a cricket match, the average runs of a battery are usually shown. This is done to give a brief idea of how well the cricketer plays according to the performances of his past matches. Similarly, a student with a high average is considered to be a good student while a student with a lower average is considered to be weak in academics. The average is given to provide a brief idea of the overall performance of an individual. However, mean and mean formulas can be used in a variety of places in a variety of ways. 

What is mean in math?

According to mathematics, it means a quantity that has an intermediate value and that is present between the highest and the lowest value. There are a plethora of means present mathematically and the process of calculating each type of mean depends on the relationship of a value with another value that is present inside the set of values. In the case of arithmetic mean, the mean is denoted with the alphabet x, in a set that consists of n number of values. Therefore, x1, x2, x3,…..,xn can be defined as the total number of the numbers being divided by n.

Uses of mean

The mean when defined in terms of arithmetic can be stated as an approximate point at which the numbers balance. For instance, if units of masses are located on a line at different points that coordinates, x1, x2,….xn, then, in that case, the mean in terms of arithmetic, will be the coordinate that is placed in the center of the system. According to the statistics, the arithmetic mean can be used as the only value that is typical of a set of data. In the case of a system that has particles that have unique masses, the center of gravity is estimated by a generalized average, the weighted mean (arithmetic). For instance, suppose a number (x) is taken to make a corresponding positive weight (w), the weighted form of arithmetic mean will be defined as the overall total of the products (wx) divided by the total of their weights. In such a case, the weighted arithmetic mean is also used in the analysis of the data that has been grouped statistically. Each number (xi), is the point that is present in the middle of an interval, and every corresponding value of (wi) is the total amount of data points present within that interval. 

Mean formula and examples

Mean can be calculated from any given set of data and hence has a specific mean formula to calculate it. The process of calculating the mean from data will solely depend on the characteristics of data that is present. For instance, if five different squares are given that have the sides 1cm, 1cm, 2cm, 5cm, and 7cm, the average area of these squares will be (12+12+22+52+72)/5 which when further calculated, will provide the value 16 square cm, with the area of one side of a square being 4cm. Therefore, the number 4 is the mean quadratically of the set of numbers, 1,1,2,5, and 7, and therefore, this means is not the same as the arithmetic mean. As arithmetic mean would have been 31/5. The mean formula therefore is the key to crack such mathematical problems. 

Geometric mean

There is also another type often called geometric mean. The geometric mean is denoted by the alphabet g and it is the geometric mean of x1 and x2. In a sequence of numbers, x1,x2,……xn, the geometric mean will be the product’s nth root. 

Conclusion

There are different types of the mean present in mathematics and each type of mean has a use in a special condition. Therefore, the process of calculating mean will differ according to the problem and the user must have a proper understanding of mean to determine the correct type of mean that is to be used. Mean has a vast usage and holds an important position in other scientific subjects as well.