geometric_mean: Geometric Mean
In umx: Structural Equation Modeling and Twin Modeling in R

geometric_mean

R Documentation

Geometric Mean

Description

The Geometric mean is the nth-root of the product of n input values. Common uses include:

Compound Annual Growth Rate (CAGR) & Financial Returns: Averaging investment yields over multiple periods. The arithmetic mean overstates performance when volatility is present (e.g., a +50% gain followed by a -50% loss leaves you with a 25% loss, even though the arithmetic average is 0%; the geometric mean correctly yields -29.29% per period, totaling -25%).
Utilitarian evaluation of value. For example, the geometric mean utility of c(1, 2, 10) is

(1 * 2 * 10)^\frac{1}{3}

= 2.7 not the arithmetic mean: 4.3.
Proportional Scaling: Proportional growth of organisms and log-normally distributed physical phenomena.
Normalizing metrics measured on different scales: e.g., computer hardware so no single benchmark disproportionately skews the score.

Usage

geometric_mean(x, na.rm = c(TRUE, FALSE))

Arguments

`x`	A vector of values.
`na.rm`	Remove NAs (default = TRUE). If FALSE, NA input returns NA (like `mean()`).

Details

The geometric mean is defined as the n-th root of the product of n numbers:

G = \left( \prod_{i=1}^{n} x_i \right)^{\frac{1}{n}} = \sqrt[n]{x_1 x_2 \cdots x_n}

In practice, to prevent numerical overflow or underflow with large vectors, it is calculated via the logarithmic transform:

\ln G = \frac{1}{n} \sum_{i=1}^{n} \ln(x_i) \implies G = \exp\left( \frac{1}{n} \sum_{i=1}^{n} \ln(x_i) \right)

Value

Geometric mean of x

References

https://en.wikipedia.org/wiki/Geometric_mean

Examples

geometric_mean(c(1.02, 1.03, 1.1))
# = 1.049

# For a given sum, geometric mean is maximised when all values are equal:
geometric_mean(c(75,75))
geometric_mean(c(50, 100))

v = c(1, 149, 500); round(c(geometric_mean(v), mean(v), median(v)), 0)
# 42 217 149

# Alternate form using mean of the logs
exp(mean(log(c(50, 100))))

# Underlying logic
sqrt(50 * 100)

# Reciprocal duality
1/geometric_mean(c(100, 50))
geometric_mean(c(1/100, 1/50))

# Missing data are dropped by default (na.rm = TRUE)
geometric_mean(c(50, 100, NA)) # 70.7
# With na.rm = FALSE, NA input gives NA, like mean()
geometric_mean(c(50, 100, NA), na.rm = FALSE) # NA
## Not run: 
# Non-positive input is an error, even alongside NAs
geometric_mean(c(50, -100))
geometric_mean(c(50, -100, NA))

## End(Not run)

umx documentation built on Oct. 11, 2026, 5:07 p.m.