# What is Arithmetic Mean in Math?

Arithmetic Mean (or simply called Mean) is a measure that determinants a value (observation) of the variable under study by dividing the sum of all values (observations) of the variable by the number of observations. We denote Arithmetic mean by x̄ .in symbol we define:

Arithmetic mean of n observation= Sum of all values of observation/No. of observation

**x̄= ∑x/n**

**Computation of Arithmetic Mean**

There are two types of data

- Ungroup data
- Group data

We, therefore, have different methods to determine, Mean for two types of data .there are explained with the help of an example.

**Ungroup data**

For ungroup data we use three approaches to find mean.

**Calculation of arithmetic mean by Direct method**

The formula under this method is given by:

Mean =sum of all observations/No.of observation

**For example,** The marks of seven students in mathematics are as a fellow. Calculate the arithmetic mean

No.of students | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

Marks | 45 | 60 | 74 | 58 | 65 | 63 | 49 |

**Solution: **let X=marks of a student

n=7

By using formula

Arithmetic mean =

Sum of all observation /no.observations

x̄= ∑x/n

Arithmetic mean = x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}+x_{7}/7

Arithmetic mean = 45+60+74+58+65+63+49/7

Arithmetic mean =414/7

Arithmetic mean =59.14 marks

Explanation: since the unit of data marks, so the result is also in marks .hence we may say that each of the seven students obtained 59 marks on average.

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