The relation between, AM, GM and HM is
The relation between, AM, GM and HM is Correct Answer AM <span style="color: rgb(32, 33, 36); ">≥ GM ≥ HM</span>
Formula
Mean = ∑xi/n
GM = N√x1 × x2 × --------xN)
HM = N/∑(1/xi)
Calculation
Let us take an observation 4, 6, 2
Arithmetic mean = (4 + 6 + 2)/3
∴ Mean = 12/3 = 4
Harmonic mean = It is reciprocal of AM
∴ HM = 1/4
GM = √AM × HM)
GM = √4 × 1/4)
∴ GM = 1
From this result we can say that AM > GM > HM
When we take some other observation which follows AM = GM = HM
∴ The relation between AM, GM, and HM is AM ≥ GM ≥ HM
Important Points
1 - Arithmetic mean
The arithmetic mean is denotted by X̅ is given by
X̅ = (x1 + x2 + ------ xn)/n
X̅ = ∑xi/n
Where as (x1 + x2 + ------ xn) are observations
n = Number of observation
2 - Geometric mean
The geometric mean is defined as the Nth square root of product of N observations and geometric mean is denotted by G
G = N√x1 × x2 × --------xN)
3 - Harmonic mean
The harmonic mean is the reciprocal of the arithmetic mean. The HM of N observation x1, x2, -----xN is
H = 1/1/N∑(1/xi) or N/∑(1/xi)
4 - The Geometric mean = √(Arithmetic mean × Harmonic mean)
5 - The value of AM s always greater than GM and HM
