# Grouped Data Arithmetic Mean Calculator

Find the average mean for the group data for given values.

Arithmetic mean Can be used for calculating statistics for grouped numbers. To find the arithmetic mean we sum all the values in the series divided by the total numbers of values in the series.

## Formula

Arithmetic Mean = ΣfX/Σf

Where,

X = Individual Score

f = Frequency

Let’s take the example of a group of kids (upto age 9) as follows where grouping is done on their age:

Age Group | Nos of Kids |

0 to 3 | 0 |

3 to 5 | 6 |

5 to 7 | 5 |

7 to 9 | 6 |

So we need X (mid point) means average of age for each group which is shown below:

Age Group | Nos of Kids(f) | X-Value |

0 to 6 | 0 | 1.5 |

3 to 5 | 6 | 4.0 |

5 to 7 | 5 | 6.0 |

7 to 9 | 6 | 8.0 |

now find ΣfX and Σf as shown below:

Age Group | Nos of Kids(f) | X-Value | fX |

0 to 3 | 0 | 1.5 | 1.5 x 0 = 0 |

3 to 5 | 6 | 4.0 | 4.0 x 6 = 24 |

5 to 7 | 5 | 6.0 | 6.0 x 5 = 30 |

7 to 9 | 6 | 8.0 | 8.0 x 6 = 48 |

Σf = 17 | ΣfX= 102 |

Now, Substitute in the above formula given

Arithmetic mean = ΣfX/Σf = 102/17 = 6