# Grouped Data Arithmetic Mean Tutorial

## Grouped Data Arithmetic Mean Tutorial

##### Grouped Data Arithmetic Mean Definition:

Data arising from organising n observed values into a smaller number of disjoint groups of values, and counting the frequency of each group; often presented as a frequency table.

##### Grouped Data Arithmetic Mean Example:

To find the Arithmetic Mean of 1,2,3,1,2,3,2.
The arithmetic mean = 1+2+3+1+2+3+2/7 = 14/7 = 2
In this case there are two 1's, three 2's and two 3's. The number of times each number occurs is called its frequency. This can be clearly given in a table as below.

X Value | Frequency(f) | ΣfX |

1 | 2 | 1 * 2 = 2 |

2 | 3 | 2 * 3 = 6 |

3 | 2 | 3 * 2 = 6 |

###### Step 1:

Find Σf.
Σf = 7

###### Step 2:

Now, find ΣfX.
ΣfX = ((1*2)+(2*3)+(3*2)) = 14

###### Step 3:

Now, Substitute in the above formula given
Arithmetic mean = ΣfX/Σf = 14/7 = 2
The above example will lead you to calculate the Grouped data Arithmetic Mean manually.

This tutorial will help you dynamically to find the Grouped data Arithmetic Mean problems.