The harmonic mean (HM) is a type of average that gives more weight to smaller values. It is calculated by dividing the total number of values by the sum of the reciprocals of those values. The harmonic mean is useful when working with rates, speeds, and ratios.
The full form of HM is Harmonic Mean. In Hindi, HM ka full form is हरमोनिक मीन.
The formula to calculate the harmonic mean (HM) is:
HM = n / [(1/a1) + (1/a2) + (1/a3) + ... + (1/an)]
| Type | Formula |
| Arithmetic Mean (AM) | AM = (y1 + y2 + y3 + ... + yn) / n |
| Geometric Mean (GM) | GM = (y1 × y2 × y3 × ... × yn)^(1/n) |
| Harmonic Mean (HM) | HM = n / [(1/y1) + (1/y2) + (1/y3) + ... + (1/yn)] |
The relationship between these means is: GM² = AM × HM
Find the harmonic mean for 3, 4, 6, and 8.
| Number | Reciprocal |
| 3 | 0.333 |
| 4 | 0.25 |
| 6 | 0.167 |
| 8 | 0.125 |
Sum of reciprocals = 0.333 + 0.25 + 0.167 + 0.125 = 0.875
HM = 4 / 0.875 = 4.57
Find the HM for the following data:
| Value (x) | Frequency (f) | Reciprocal (1/x) | f/x |
| 2 | 1 | 0.5 | 0.5 |
| 5 | 3 | 0.2 | 0.6 |
| 3 | 7 | 0.333 | 2.334 |
| 6 | 3 | 0.167 | 0.5 |
| 8 | 9 | 0.125 | 1.125 |
| 7 | 4 | 0.143 | 0.57 |
Total frequency (N) = 27
Sum of f/x = 5.635
HMw = 27 / 5.635 = 4.791
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The formula for HM (Harmonic Mean) is: HM = n / (1/x1 + 1/x2 + ... + 1/xn), where x1, x2, ... xn are the values in the dataset.
The full forms are: HM: Harmonic Mean DM: It can refer to various things, like Data Management or Duty Manager, depending on the context.
Whether GM (Geometric Mean) is greater than HM depends on the data; it can be greater, smaller, or equal, depending on the values.