Question

Arithmetic average of real nonnegative numbers is always smaller than or equal to geometric average. Group of answer choices True False

Answer 1

Answer:

False

Step-by-step explanation:

Actually, the arithmetic average (or mean) is always greater or equal than the geometric average. This is known as the Arithmetic-Geometric inequality (AM inequality). Let a,b be two real numbers, then the AM inequality states that

$\frac{a+b}{2}\geq \sqrt{ab}$

To see that the given statement is false, consider a=1, b=3. The arithmetic mean is equal to (1+3)/2=2, and the geometric mean is equal to $\sqrt{1\cdot 3}=\sqrt{3}$ but $2>\sqrt{3}$, contrary to the statement (arithmetic>geometric in this case).