__What is Harmonic Mean?__

__What is Harmonic Mean?__

Harmonic Mean is also a mathematical average but is limited in its application. It is generally used to find average of variables that are expressed as a ratio of two different measuring units e. g. speed is measured in km/hr or miles/sec etc.

__Weighted Harmonic Mean__

__Weighted Harmonic Mean__

**Formula**

H.M.=W∑(WX)H.M.=W∑(WX)

Where −

· H.M.H.M. = Harmonic Mean

· WW = Weight

· XX = Variable value

**Example**

**Problem Statement:**

Find the weighted H.M. of the items 4, 7,12,19,25 with weights 1, 2,1,1,1 respectively.

**Solution:**

XX | WW | WXWX |

4 | 1 | 0.2500 |

7 | 2 | 0.2857 |

12 | 1 | 0.0833 |

19 | 1 | 0.0526 |

25 | 1 | 0.0400 |

∑W∑W | ∑WX∑WX= 0.7116 |

Based on the above mentioned formula, Harmonic Mean G.M.G.M. will be:

H.M.=W∑(WX)=60.7116=8.4317H.M.=W∑(WX)=60.7116=8.4317

∴ Weighted H.M = 8.4317

We’re going to discuss methods to compute the **Harmonic Mean** for three types of series:

· Individual Data Series

· Discrete Data Series

· Continuous Data Series

__Individual Data Series__

__Individual Data Series__

When data is given on individual basis. Following is an example of individual series:

Items | 5 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |

__Discrete Data Series__

__Discrete Data Series__

When data is given alongwith their frequencies. Following is an example of discrete series:

Items | 5 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |

Frequency | 2 | 5 | 1 | 3 | 12 | 0 | 5 | 7 |

__Continuous Data Series__

__Continuous Data Series__

When data is given based on ranges alongwith their frequencies. Following is an example of continous series:

Items | 0-5 | 5-10 | 10-20 | 20-30 | 30-40 |

Frequency | 2 | 5 | 1 | 3 | 12 |