Which of the following measure possess mathematical properties? AM, GM or hM?

Question

Answer

Mathematical Properties of AM, GM, and hM

AM (Arithmetic Mean)

AM is a mathematical measure that possesses several properties.

One of the most significant properties of AM is that it is linear, which means that if we add a constant value to all the terms of a set, the AM of that set will also increase by the same constant value.

The AM of a set of numbers is always greater than or equal to the minimum value and less than or equal to the maximum value.

AM is also symmetric, which means that if we swap any two terms of a set, the AM will remain the same.

GM (Geometric Mean)

GM is another mathematical measure that has several properties.

One of the most significant properties of GM is that it is multiplicative, which means that if we multiply all the terms of a set by a constant value, the GM of that set will also increase by the same constant value.

The GM of a set of positive numbers is always greater than or equal to zero.

GM is also symmetric, which means that if we swap any two terms of a set, the GM will remain the same.

hM (Harmonic Mean)

hM is a mathematical measure that possesses several properties.

One of the most significant properties of hM is that it is not linear or multiplicative, which means that it does not follow the same rules as AM and GM.

hM is always less than or equal to the GM and AM of a set of positive numbers.

hM is also symmetric, which means that if we swap any two terms of a set, the hM will remain the same.

Conclusion

In conclusion, all three measures possess mathematical properties, but each has its unique set of properties. AM is linear and symmetric, GM is multiplicative and symmetric, and hM is not linear or multiplicative and is always less than or equal to the GM and AM of a set of positive numbers.

Answer

I think AM

Answer

All

Answer

All of the above

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