geometric mean: meaning, definition, pronunciation and examples
C1Formal, Technical, Academic
Quick answer
What does “geometric mean” mean?
A type of average calculated by multiplying n numbers together and then taking the nth root of the product.
Audio
Pronunciation
Definition
Meaning and Definition
A type of average calculated by multiplying n numbers together and then taking the nth root of the product.
A measure of central tendency used for numbers that are best interpreted as products or rates of change, often applied in finance, statistics, and various scientific fields to average ratios or percentage changes over time.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or grammatical differences. The term is identical in both varieties.
Connotations
Identical technical connotations in mathematics, statistics, and finance.
Frequency
Equally frequent in technical/academic contexts in both regions.
Grammar
How to Use “geometric mean” in a Sentence
The geometric mean of X and Y is Z.To calculate the geometric mean, multiply all values and take the nth root.Vocabulary
Collocations
Examples
Examples of “geometric mean” in a Sentence
adjective
British English
- The geometric-mean calculation is more appropriate for these growth figures.
American English
- The geometric mean return provides a more accurate picture of portfolio performance.
Usage
Meaning in Context
Business
Used in finance to calculate average investment returns over multiple periods, as it accounts for compounding.
Academic
Common in statistics, mathematics, economics, and scientific research for analysing data involving ratios, indices, or growth rates.
Everyday
Rarely used in casual conversation outside specific technical discussions.
Technical
Essential in fields like epidemiology (for antibody titres), geology (for particle size analysis), and image processing (for reducing noise).
Vocabulary
Synonyms of “geometric mean”
Neutral
Weak
Vocabulary
Antonyms of “geometric mean”
Watch out
Common Mistakes When Using “geometric mean”
- Using the geometric mean for data that can contain zero or negative values (it's only defined for positive numbers).
- Confusing it with the arithmetic mean when averaging rates of change.
- Incorrectly saying 'geometrical mean' (less common variant).
FAQ
Frequently Asked Questions
No, the geometric mean is only defined for sets of positive real numbers. An even root of a negative number is not a real number.
The arithmetic mean adds numbers and divides by the count, suitable for additive data. The geometric mean multiplies numbers and takes the nth root, suitable for multiplicative data like ratios and growth rates.
It is essential in finance for calculating compound annual growth rates (CAGR), in biology for averaging dilution titres, and in social sciences for normalising highly skewed data (via the log transformation).
Multiply the three numbers together, then take the cube root of the product. For example, the geometric mean of 2, 4, and 8 is the cube root of (2*4*8) = cube root of 64, which is 4.
A type of average calculated by multiplying n numbers together and then taking the nth root of the product.
Geometric mean is usually formal, technical, academic in register.
Geometric mean: in British English it is pronounced /ˌdʒiː.əˌmet.rɪk ˈmiːn/, and in American English it is pronounced /ˌdʒiː.əˌme.trɪk ˈmiːn/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think 'GEO-METRIC': GEO for earth/ground (a solid foundation for multiplication) and METRIC for measurement. It's the mean you use when things GROW (multiply) geometrically.
Conceptual Metaphor
BALANCING SCALE FOR PRODUCTS (If the arithmetic mean balances sums, the geometric mean balances products).
Practice
Quiz
When is the geometric mean most appropriately used?