Number of samples = 6

Geometric mean = 11.7591

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GENERATE WORK

GENERATE WORK

**Input Data : **

Data set = 3, 8, 10, 17, 24, 27

Total number of elements = 6

**Objective :**

Find what is geometric mean for given input data?

**Formula :**

**Solution :**

Geometric Mean = ^{6}√(3 x 8 x 10 x 17 x 24 x 27)

= ^{6}√(2643840)

Geometric Mean = 11.7591

** Geometric Mean Calculator** is an online tool programmed to calculate the statistical data if all the quantities had the same value, what would that value have to be in order to achieve the same product? The geometric mean is a type of mean or average, which relevant to set of quantities multiply together to produce a product.

The arithmetic mean is relevant to any time set of quantities add together to produce a total. The arithmetic mean provides the answer for if all the quantities had the same value, what would that value has to be in order to achieve the same total?

The Geometric mean of a set of data can be derived from the formula

**Geometric Mean Calculation Example**

For example, to find the geometric mean of 9, 27 and 66; The first step is to multiplying the given numbers 9 x 27 x 66 will yield the result 16038. By taking cube root of the result 16038 gives the resulting Geometric Mean 25.2184. The Cubic Root is taken because of using three numbers, if using two numbers; we had to take the square root for the resulting product. If the set of numbers increases the power of root also increase and vice versa.

The above example can help you to understand the Geometric Mean process and will be useful for calculating the Geometric Mean. In the case of larger set of data, finding out the Geometric mean manually will be bit complicated. To accomplish this task, this online Geometric Mean Calculator assists you to find out the larger sets of data by a single mouse click and user can compare the manually calculated values with this calculator's output for given data set to verify their accuracy of the manually calculated result.