Geometric Mean in Statistics

Geometric Mean in Statistics is the average obtained by multiplying all the data in a sample group, then it is rooted by the amount of the sample data.

Geometric Mean Formulas in Statistics

U = ⁿ√(x₁ . x₂ . x₃ . ... . x_n)

Information :

U = geometric mean value
x = data

n = amount of data

Example :

Please determine geometric mean of 2,4,8,16 !

Answer :

n = 4

x₁ = 2

x₂ = 4

x₃ = 8

x₄ = 16

U = ⁴√(x₁ . x₂ . x₃ . x₄)

U = ⁴√(2 . 4 . 8 . 16)

U = ⁴√(2¹ . 2² . 2³ . 2⁴)

U = ⁴√(2^1+2+3+4)

U = ⁴√2¹⁰

U = 2^10/4

U = 2^5/2

U = √2⁵

U = √32

U = √(16 x 2)

U = √16 x √2

U = 4√2