Comprehensive Calculator Guide
This calculator finds the geometric mean of positive numbers, the nth root of their product, and compares it with the arithmetic mean. The geometric mean of 2, 8 and 32 is 8, against an arithmetic mean of 14. It is the right average for growth: +10%, +50%, −20% averages about 9.7% a year, not 13.3%.
Geometric mean
Multiply the values and take the root of their count. Use it for quantities that compound, entering growth as factors (1.1 for +10%). It is never above the arithmetic mean.
How to Use
- Enter positive numbers separated by commas or spaces.
- Enter growth as factors: 1.1, 0.8.
- Press “Calculate” to see the geometric mean and the arithmetic mean.
Formula Used
(x₁ × x₂ × … × xₙ)^(1/n)
Practical Examples
- Example 1
- 2, 8, 32: 8.
- Example 2
- 1.1, 1.5, 0.8: about 1.097.
Important Tips
- Convert percentages to factors.
- Arithmetic for sums, geometric for products.
- Two values: √(ab).
Common Mistakes to Avoid
- Averaging growth arithmetically.
- Entering 10, 50, −20.
- Using zero or negatives.
Frequently Asked Questions
- 4 and 9?
- 6.
- Why for returns?
- Returns compound.
- Can it exceed the arithmetic mean?
- No.