Question

The average of three real numbers is greater than or equal to at least one of the numbers.

Answer 1

Answer:

The given statement is true.        

Step-by-step explanation:

We are given the following information in the question:

The average of three real numbers is greater than or equal to at least one of the numbers.

We can prove this statement.

Let a, b and c be the three real numbers.

Then, the average of these three real numbers is given by

$\text{Average} = \displaystyle\frac{\text{Sum of all observation}}{\text{Total number of observation}}\\\\A = \frac{a+b+c}{3}\\\\3A = a + b + c$

Let a be the smallest of the three natural number.

Then, we can write,

$a + b+c \geq a+a+a\\3A \geq 3a\\A\geq a$

Let a be the largest number.

$a + b+c \leq a+a+a\\3A \leq 3a\\A\leq a$

Thus, looking at both the inequalities, we can say that the average of three real numbers is greater than or less than equal to one of the numbers.