Harmonic mean (H.M)

Harmonic mean (H.M)

    • Harmonic mean of a set of observations is defined as the reciprocal of the arithmetic average of the reciprocal of the given values. If x1,x2…..xn are n observations,
    H.M
    • For a frequency distribution
    H.M
    • H.M is used when we are dealing with speed, rates, etc.
    Example 13
    • From the given data 5,10,17,24,30 calculate H.M.
    0.4338=11.526

    Example 14
    • Number of tomatoes per plant are given below. Calculate the harmonic mean.
    Number of tomatoes per plant 20 21 22 23 24 25
    Number of plants 4 2 7 1 3 1

    H.M.jpg21.91

    Merits of H.M

    1. It is rigidly defined.
    2. It is defined on all observations.
    3. It is amenable to further algebraic treatment.
    4. It is the most suitable average when it is desired to give greater weight to smaller observations and less weight to the larger ones.

    Demerits of H.M

    1. It is not easily understood.
    2. It is difficult to compute.
    3. It is only a summary figure and may not be the actual item in the series
    4. It gives greater importance to small items and is therefore, useful only when small items have to be given greater weightage.
    5. It is rarely used in grouped data.

Last modified: Friday, 16 March 2012, 6:58 PM