# How to calculate the estimated mean and estimated median of grouped data?

Age | Mid of age | Frequency | Mid * Frequency |

21 – 25 | 23 | 5 | 23 * 5 = 115 |

26 – 30 | 28 | 2 | 28 * 2 = 56 |

31 – 35 | 33 | 6 | 33 * 6 = 198 |

35 – 40 | 37 | 8 | 37 * 8 = 296 |

Total | 21 | 665 |

**Estimated Mean** = 665 / 21

** ** = 31.66

**Class intervals:**

Group 21 to 25, 26 to 30, 31 to 35 and 35 to 40 are class intervals.

Mean is 31.6 so 31.6 rounds to 32.

**Estimated mean **= 32

**Median group** = 31 to 35

**Estimated Median** = ?

**Estimated Median** = L + (TV / 2) – SBM ⁄ FMG * GW

L = Lower boundary of median group | 30.5 |

TV = Total number of values | 21 |

SBM = Sum of frequencies before median group | 7 |

FMG = Frequency of median group | 6 |

GW = Group width | 5 |

**Result:** Our median group is 31 to 35 and yes estimated median 33.4 is in the median group.

**How to calculate the estimated mode of the above-grouped data?**

L = Lower boundary of median group | 30.5 |

SBM = sum of frequencies before median group | 7 |

FMG = Frequency of median group | 6 |

FBMG = Sum of frequencies of all groups before median group | 7 |

FBMG = Sum of frequencies of all groups after median group | 8 |

GW = Group width | 5 |

**Mode:** Mode is the most occurring Value in the data.