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Home > Statistical Methods calculators > Geometric mean, Harmonic mean for ungrouped data example
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Harmonic mean Example for ungrouped data
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- Formula & Example
- Geometric mean Example
- Harmonic mean Example
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Other related methods
- Mean, Median and Mode
- Quartile, Decile, Percentile, Octile, Quintile
- Population Variance, Standard deviation and coefficient of variation
- Sample Variance, Standard deviation and coefficient of variation
- Population Skewness, Kurtosis
- Sample Skewness, Kurtosis
- Geometric mean, Harmonic mean
- Mean deviation, Quartile deviation, Decile deviation, Percentile deviation
- Five number summary
- Box and Whisker Plots
- Construct an ungrouped frequency distribution table
- Construct a grouped frequency distribution table
- Maximum, Minimum
- Sum, Length
- Range, Mid Range
- Stem and leaf plot
- Ascending order, Descending order
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3. Harmonic mean Example
1. Calculate Harmonic mean from the following data
`3,13,11,15,5,4,2`
Solution:
Harmonic mean :
| `x` | `1/x` | | 3 | 0.3333 | | 13 | 0.0769 | | 11 | 0.0909 | | 15 | 0.0667 | | 5 | 0.2 | | 4 | 0.25 | | 2 | 0.5 | | --- | --- | | `sum 1/x=1.5178` |
HM of X `= n/(sum (f/x))`
`=(7)/(1.5178)`
`=4.6118`
2. Calculate Harmonic mean from the following data
`10,50,30,20,10,20,70,30`
Solution:
Harmonic mean :
| `x` | `1/x` | | 10 | 0.1 | | 50 | 0.02 | | 30 | 0.0333 | | 20 | 0.05 | | 10 | 0.1 | | 20 | 0.05 | | 70 | 0.0143 | | 30 | 0.0333 | | --- | --- | | `sum 1/x=0.401` |
HM of X `= n/(sum (f/x))`
`=(8)/(0.401)`
`=19.9525`
3. Calculate Harmonic mean from the following data
`73,70,71,73,68,67,69,72,76,71`
Solution:
Harmonic mean :
| `x` | `1/x` | | 73 | 0.0137 | | 70 | 0.0143 | | 71 | 0.0141 | | 73 | 0.0137 | | 68 | 0.0147 | | 67 | 0.0149 | | 69 | 0.0145 | | 72 | 0.0139 | | 76 | 0.0132 | | 71 | 0.0141 | | --- | --- | | `sum 1/x=0.141` |
HM of X `= n/(sum (f/x))`
`=(10)/(0.141)`
`=70.9105`
This material is intended as a summary. Use your textbook for detail explanation.
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