Importance of Average in Mathematics


There are a number of concepts which we come across in Mathematics, such as arithmetic operations, numbers, algebra, geometry, statistics, etc. One of the most important topics in statistics which is called average or mean. Why do we need to learn about average? What are the uses of average? How it is calculated? The answers to all these questions are given here in this article.

An average is nothing but a single value which represents a group of data. It summarises a large amount of data in a single value and denotes the deviation or variation around this single value within the given original data. One such quantity, in a statistical distribution or a set of data which is the average of the absolute values of the differences between individual entities and their mean, is called mean deviation.

In statistics, basically mean, median and mode are the central tendencies of a data set. These three measures summarise the data with a single value. We know, mean is nothing but the average of the given data set. Alternatively, mean is sometimes mentioned as average, because both are same in mathematical terms. To find the mean, we need to add all the given values in data set and divide it by a number of values. But what about median and mode?

Median is the centre value of the dataset when data is arranged in an orderly fashion, whether in ascending or descending. Whereas mode represents how frequently a number or value is repeated in the data set. Let us understand, the central tendency with the help of an example.

Example: A data set is given as 1,5,3,4,4,2,6

Mean of Average = Total of values/Number of values

= (1+5+3+4+4+2+6)/7 = 25/7

Median is the centre value of data when arranged in an order. So, on arranging the given data in ascending order, we get;


Therefore, Median = 4

A mode is a value which has a higher number of frequency. As we can see here, 4 is repeated in the data two times.

Therefore, Mode = 4

So we have known the importance of learning ‘mean’ along with median and mode in statistics. In a broad way, the mean is of three types, they are Arithmetic mean, Geometric Mean and Harmonic Mean. Arithmetic is the basic mean where we find the average of the given data set.  A Geometric Mean is the average value or mean which signifies the central tendency of the set of values by finding the product of their values. The harmonic mean is the reciprocal of the arithmetic mean.

The average is the basic term used when we do simple calculations. For example, if we have to find the average sale of 10 products, then we need to sum up the prices of all the ten products and divide it by 10 to get the average. Hence, it is important to learn about average or mean and its related concepts. Although, the advanced concept of the mean are majorly used in large scale industries, for small scale just knowing the basics is sufficient.

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