Harmonic Mean given Arithmetic and Geometric Means Calculator

✖Geometric Mean is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values.ⓘ Geometric Mean [GM]			+10% -10%
✖Arithmetic Mean is the average value or mean which signifies the central tendency of the set of numbers by finding the sum of their values.ⓘ Arithmetic Mean [AM]			+10% -10%

✖Harmonic Mean is the average value or mean which signifies the central tendency of the set of numbers by finding the reciprocal of their values.ⓘ Harmonic Mean given Arithmetic and Geometric Means [HM]

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Formula

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Harmonic Mean given Arithmetic and Geometric Means

Formula

`"HM" = ("GM"^2)/"AM"`

Example

`"48.02"=(("49")^2)/"50"`

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Harmonic Mean given Arithmetic and Geometric Means Solution

STEP 0: Pre-Calculation Summary

Formula Used

Harmonic Mean = (Geometric Mean^2)/Arithmetic Mean
HM = (GM^2)/AM
This formula uses 3 Variables

Variables Used

Harmonic Mean - Harmonic Mean is the average value or mean which signifies the central tendency of the set of numbers by finding the reciprocal of their values.
Geometric Mean - Geometric Mean is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values.
Arithmetic Mean - Arithmetic Mean is the average value or mean which signifies the central tendency of the set of numbers by finding the sum of their values.

STEP 1: Convert Input(s) to Base Unit

Geometric Mean: 49 --> No Conversion Required
Arithmetic Mean: 50 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

HM = (GM^2)/AM --> (49^2)/50

Evaluating ... ...

HM = 48.02

STEP 3: Convert Result to Output's Unit

48.02 --> No Conversion Required

FINAL ANSWER

48.02 <-- Harmonic Mean

(Calculation completed in 00.004 seconds)

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Created by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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St Joseph's College (SJC), Bengaluru

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< 6 Harmonic Mean Calculators

Harmonic Mean of Four Numbers

Go Harmonic Mean = 4/(1/First Number+1/Second Number+1/Third Number+1/Fourth Number)

Harmonic Mean of Two Numbers

Go Harmonic Mean = (2*First Number*Second Number)/(First Number+Second Number)

Harmonic Mean of Three Numbers

Go Harmonic Mean = 3/(1/First Number+1/Second Number+1/Third Number)

Harmonic Mean of N Numbers

Go Harmonic Mean = Total Numbers/Harmonic Sum of Numbers

Harmonic Mean given Arithmetic and Geometric Means

Go Harmonic Mean = (Geometric Mean^2)/Arithmetic Mean

Harmonic Mean of Reciprocal of First N Natural Numbers

Go Harmonic Mean = 2/(Total Numbers+1)

Harmonic Mean given Arithmetic and Geometric Means Formula

Harmonic Mean = (Geometric Mean^2)/Arithmetic Mean
HM = (GM^2)/AM

What is Harmonic Mean?

Harmonic Mean is basically the average value or mean which signifies the central tendency of the set of numbers by finding the reciprocal of their values. It is calculated by dividing the total count of numbers by the harmonic sum or the sum of reciprocals of the numbers. In many situations involving rates and ratios, the Harmonic Mean provides the correct average.

How to Calculate Harmonic Mean given Arithmetic and Geometric Means?

Harmonic Mean given Arithmetic and Geometric Means calculator uses Harmonic Mean = (Geometric Mean^2)/Arithmetic Mean to calculate the Harmonic Mean, Harmonic Mean given Arithmetic and Geometric Means formula is defined as the average value or mean which signifies the central tendency of the set of numbers by finding the reciprocal of their values, and calculated using the arithmetic mean and geometric mean of them. Harmonic Mean is denoted by HM symbol.

How to calculate Harmonic Mean given Arithmetic and Geometric Means using this online calculator? To use this online calculator for Harmonic Mean given Arithmetic and Geometric Means, enter Geometric Mean (GM) & Arithmetic Mean (AM) and hit the calculate button. Here is how the Harmonic Mean given Arithmetic and Geometric Means calculation can be explained with given input values -> 48.02 = (49^2)/50.

FAQ

What is Harmonic Mean given Arithmetic and Geometric Means?

Harmonic Mean given Arithmetic and Geometric Means formula is defined as the average value or mean which signifies the central tendency of the set of numbers by finding the reciprocal of their values, and calculated using the arithmetic mean and geometric mean of them and is represented as HM = (GM^2)/AM or Harmonic Mean = (Geometric Mean^2)/Arithmetic Mean. Geometric Mean is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values & Arithmetic Mean is the average value or mean which signifies the central tendency of the set of numbers by finding the sum of their values.

How to calculate Harmonic Mean given Arithmetic and Geometric Means?

Harmonic Mean given Arithmetic and Geometric Means formula is defined as the average value or mean which signifies the central tendency of the set of numbers by finding the reciprocal of their values, and calculated using the arithmetic mean and geometric mean of them is calculated using Harmonic Mean = (Geometric Mean^2)/Arithmetic Mean. To calculate Harmonic Mean given Arithmetic and Geometric Means, you need Geometric Mean (GM) & Arithmetic Mean (AM). With our tool, you need to enter the respective value for Geometric Mean & Arithmetic Mean and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Harmonic Mean?

In this formula, Harmonic Mean uses Geometric Mean & Arithmetic Mean. We can use 5 other way(s) to calculate the same, which is/are as follows -

Harmonic Mean = (2*First Number*Second Number)/(First Number+Second Number)
Harmonic Mean = Total Numbers/Harmonic Sum of Numbers
Harmonic Mean = 3/(1/First Number+1/Second Number+1/Third Number)
Harmonic Mean = 4/(1/First Number+1/Second Number+1/Third Number+1/Fourth Number)
Harmonic Mean = 2/(Total Numbers+1)

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