THOUGHT PROVOKING To find the arithmetic mean of n numbers, divide the sum of the numbers by n. To find the geometric mean of n numbers a_(1),a_(2),a_(3),ldots .a_(n) take the n th root of the product of the numbers. geometric mean=sqrt [n](a_(1)cdot a_(2)cdot a_(3)cdot ldots cdot a_(n)) Compare the arithmetic mean to the geometric mean of n numbers. The geometric mean is always square the arithmetic mean. : less than greater than : greater than or equal to less than or equal to : equal to

## Step 1The arithmetic mean and the geometric mean of a set of numbers are two different ways to measure the central tendency of the data. The arithmetic mean is calculated by adding all the numbers and dividing by the number of numbers. The geometric mean, on the other hand, is calculated by multiplying all the numbers and then taking the n-th root of the product.## Step 2The arithmetic mean of a set of numbers is given by the formula:### ## Step 3The geometric mean of a set of numbers is given by the formula:### \( (a1 \cdot a2 \cdot a3 \cdot ... \cdot an)^{\frac{1}{n}} \)## Step 4The relationship between the arithmetic mean and the geometric mean of a set of numbers is defined by the AM-GM inequality. The AM-GM inequality states that for any set of non-negative real numbers, the arithmetic mean is always greater than or equal to the geometric mean.