MathDB

4

Part of 1997 Baltic Way

Problems(1)

Arithmetic mean a of x_i

Source: Baltic Way 1997

1/28/2011
Prove that the arithmetic mean aa of x1,…,xnx_1,\ldots ,x_n satisfies (x1−a)2+…+(xn−a)2≤12(∣x1−a∣+…+∣xn−a∣)2 (x_1-a)^2+\ldots +(x_n-a)^2\le \frac{1}{2}(|x_1-a|+\ldots +|x_n-a|)^2
inequalitiesinequalities proposed