Question

if GM is 18 and AM is 27 then HM is

Answer 1

Answer:

The HM is $12$.

Step-by-step explanation:

It is given that GM is $18$

and AM is $27$

We need to determine HM.

The geometric mean is the average of a set of products.

The calculation of GM is commonly used for determination of the performance results of given sequence.

Here, GM=$18$

The arithmetic mean is the quantity obtained by summing of two or more numbers or variables and then dividing by the number of numbers or variables.

Here, AM=$27$.

Harmonic mean is calculated by dividing the number of observations by the reciprocal of each number in the series.

The relation between three of them is

$GM^{2} =AM*HM$

Putting values

$18^{2} =27*HM$

$HM=\frac{324}{27}$

$HM=12$

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Answer 2

Answer:

The value of HM is 12.

Step-by-step explanation:

Concept:-

Arithmetic mean (AM): The sum of all the values divided by the total number of values is known as the arithmetic mean.

Geometric mean (GM): The nth root of product of all the given values is known as the geometric mean.

Harmonic mean (HM): The reciprocal of the arithmetic mean is known as the harmonic mean.

Relation between AM, GM and HM is,

$AM\times HM = GM^2$ . . . . . (1)

Step 1 of 1

According to the question,

Given: GM = 18 and AM = 27

To find the value of HM.

Substitute the values 18 for GM and 27 for AM in the relation (1) as follows:

⇒ 27 × HM = $18^2$

⇒ HM = $\frac{18\times18}{27}$

⇒ HM = 12

Therefore, the value of HM is 12.

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Answer 3

Answer:

The value of Harmonic Mean $H.M = 12$

Step-by-step explanation:

• Arithmetic Mean (AM) :

The arithmetic mean, also known as the mean or average, is the amount obtained by adding two or more numbers or variables together and then dividing by the number of numbers or variables.

• Geometric Mean (GM):

The Geometric Mean (G.M) of a chain containing $n$ observations is the $nth$ root of the made of the values.

• Harmonic Mean (HM) :

The Harmonic Mean (HM) is described because the reciprocal of the common of the reciprocals of the statistics values. It is primarily based totally on all of the observations.

• There is an important relationship between $G.M , H.M , A.M$.

$(GM)^{2} = HM * AM$

Given,

$AM = 27$

$GM = 18$

Subsituting these values,

$(GM)^{2} = HM * AM$

we get,

$(18)^{2} = 27 *HM$

$H.M = \frac{18*18}{27}$

$H.M = \frac{324}{27}$

$H.M = 12$

Therefore, the value of Harmonic Mean $H.M = 12$

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