Mean Calculator
Calculate arithmetic, geometric, harmonic, and weighted means with detailed explanations and statistical insights
Data Input
Enter positive numbers for geometric and harmonic means
Results
Enter data values and click "Calculate Mean" to see the results
Understanding Different Types of Means
Arithmetic Mean
The most common type of average. Simply add all values and divide by the count of values.
Geometric Mean
Used for rates, percentages, and multiplicative processes. Takes the nth root of the product of all values.
Harmonic Mean
Used for rates and ratios. Calculated as the reciprocal of the arithmetic mean of reciprocals.
Weighted Mean
Gives different importance (weights) to different values based on their significance.
When to Use Each Mean
Arithmetic Mean
- • Test scores and grades
- • Temperature readings
- • Height and weight measurements
- • General statistical analysis
Geometric Mean
- • Investment returns
- • Population growth rates
- • Inflation rates
- • Index calculations
Harmonic Mean
- • Average speed calculations
- • Financial ratios (P/E ratios)
- • Resistance in parallel circuits
- • Machine learning (F1 score)
Weighted Mean
- • Course grades with credits
- • Portfolio performance
- • Survey responses
- • Quality control metrics
Key Properties
- • HM ≤ GM ≤ AM (inequality)
- • Arithmetic most sensitive to outliers
- • Harmonic least affected by large values
- • Geometric best for multiplicative data
Common Mistakes
- • Using arithmetic for rates
- • Negative values in geometric/harmonic
- • Wrong weights in weighted mean
- • Ignoring data distribution
Applications
- • Statistical analysis
- • Financial modeling
- • Engineering calculations
- • Academic grading
- • Performance metrics
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