Question

the geometric mean of the numbers 4,6 and 9 is?
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Answer 1

Answer:

6

Step-by-step explanation:

Geometric Mean of 4,6,9 = (4*6*9)^1/3 = (216)^1/3 = 6

Answer 2

Answer:

The geometric mean of the numbers 4,6 and 9 is 6.

Step-by-step explanation:

Geometric Mean (GM) is the average value or mean that, by calculating the product of the values of a set of numbers, denotes the central tendency of the data. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.

The nth root of the product of n numbers is what is known as the geometric mean. The geometric mean differs from the arithmetic mean, as is noted. As a result of the fact that in arithmetic mean, the data values are added before being divided by the total number of values. However, when calculating the geometric mean, we multiply the provided data values before taking the root of the entire number of data values using the radical index. Take the square root, for instance, if there are two data points, the cube root if there are three, the fourth root if there are four, and so on.

$G.M=\sqrt[n]{x_{1} \times x_{2}.....x_{n} }$

Given: Numbers 4,6,9

Take cube root of given number to find geometric mean of the numbers.

$G.M=\sqrt[3]{4\times 6\times 9} \\G.M=\sqrt[3]{2\times2\times2\times3\times3\times3} \\G.M=2\times3\\G.M=6$

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