# Average

An **average** of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. In terms of statistics, the average of a given set of numerical data is also called mean.

For example, the average of 2, 3 and 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the central value of 2,3 and 4. Thus, the meaning of average is to find the mean value of a group of numbers.

Average = Sum of Values/Number of Values

## Average Symbol

The average is basically the mean of the values which are represented by x̄. It is also denoted by the symbol ‘μ’.

## Average Formula

The formula to find the average of given numbers or values is very easy. We just have to add all the numbers and then divide the result by the number of values given. Hence, the average formula in Maths is given as follows:

**Average = Sum of Values/ Number of values**

Suppose, we have given with n number of values such as x_{1}, x_{2}, x_{3} ,….., x_{n}. The average or the mean of the given data will be equal to:

**Average = (x _{1}+x_{2}+x_{3}+…+x_{n})/n**

## How to Calculate Average?

We can easily calculate the average for a given set of values. We just have to add all the values and divide the outcome by the number of given values.

Average can be calculated using three simple steps. They are:

**Step 1: Sum of Numbers: **

The first step in finding the average of numbers is to find the sum of all the given numbers.

**Step 2: Number of Observations:**

Next, we have to count how many numbers are in the given dataset.

**Step 3: Average Calculation:**

The final step in calculating the average is to divide the sum by the number of observations.

### Arithmetic Mean

The Arithmetic mean is the most common type of Average. If n numbers are given, each number denoted by ai(where i = 1,2, …, n), the arithmetic mean is the sum of the as divided by n, then:

### Geometric Mean

The geometric mean is a method to find the central tendency of a set of numbers by finding the nth root of the product of n numbers. It is completely different from the arithmetic mean, where we add the observations and then divide the sum by the number of observations. But in geometric mean, we find the product of all the observations and then find the nth root of the product, provided that n is number of observations.

The Geometric Mean (G.M) of a data set containing n observations is the n^{th} root of the product of the values.

the geometric mean of **n** numbers **a _{1} to a_{n}** is:

^{n}√(a_{1} × a_{2} × ... × a_{n})

### Harmonic Mean

The harmonic mean is defined as the reciprocal of the average of the reciprocals of the given data values.

The formula to find the harmonic mean is given by:

Harmonic Mean, HM = n / [(1/x_{1})+(1/x_{2})+(1/x_{3})+…+(1/x_{n})]

Where x_{1}, x_{2}, x_{3},…, x_{n} are the individual items up to n terms.