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Home > Statistical Methods calculators > Geometric mean, Harmonic mean for ungrouped data example
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Geometric 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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2. Geometric mean Example
1. Calculate Geometric mean from the following data
`3,13,11,15,5,4,2`
Solution:
Geometric mean :
| `x` | `log(x)` | | 3 | 0.4771 | | 13 | 1.1139 | | 11 | 1.0414 | | 15 | 1.1761 | | 5 | 0.699 | | 4 | 0.6021 | | 2 | 0.301 | | --- | --- | | `sum log(x)=5.4106` |
GM of X `= Antilog((sum flog(x))/n)`
`= Antilog((5.4106)/(7))`
`= Antilog(0.7729)`
`= 5.9285`
2. Calculate Geometric mean from the following data
`10,50,30,20,10,20,70,30`
Solution:
Geometric mean :
| `x` | `log(x)` | | 10 | 1 | | 50 | 1.699 | | 30 | 1.4771 | | 20 | 1.301 | | 10 | 1 | | 20 | 1.301 | | 70 | 1.8451 | | 30 | 1.4771 | | --- | --- | | `sum log(x)=11.1004` |
GM of X `= Antilog((sum flog(x))/n)`
`= Antilog((11.1004)/(8))`
`= Antilog(1.3875)`
`= 24.4088`
3. Calculate Geometric mean from the following data
`73,70,71,73,68,67,69,72,76,71`
Solution:
Geometric mean :
| `x` | `log(x)` | | 73 | 1.8633 | | 70 | 1.8451 | | 71 | 1.8513 | | 73 | 1.8633 | | 68 | 1.8325 | | 67 | 1.8261 | | 69 | 1.8388 | | 72 | 1.8573 | | 76 | 1.8808 | | 71 | 1.8513 | | --- | --- | | `sum log(x)=18.5098` |
GM of X `= Antilog((sum flog(x))/n)`
`= Antilog((18.5098)/(10))`
`= Antilog(1.851)`
`= 70.9552`
This material is intended as a summary. Use your textbook for detail explanation.
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