Can the geometric mean of two positive numbers be negative?

Hence, a geometric mean cannot be negative because we can only use the formula of geometric mean for positive numbers.

What is the geometric mean of two negative numbers?

The geometric mean between two negative terms will be a negative term. Suppose we have -4 , -16 and -64. The GM of -4 and -64 = (256)^0.5 = -16. One of the square roots of 256 is 16, however, that value cannot be accepted in the present case and we have to accept the negative answer or -16.

Can you do geometric mean with negative numbers?

Like zero, it is impossible to calculate Geometric Mean with negative numbers. However, there are several work-arounds for this problem, all of which require that the negative values be converted or transformed to a meaningful positive equivalent value.

Does geometric mean have to be positive?

The geometric mean applies only to positive numbers. The geometric mean is often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as a set of growth figures: values of the human population or interest rates of a financial investment over time.

What is the geometric mean between two numbers A and B if both are negative?

if a and b are negative. (Definition 4 The geometric mean is the positive square root of the product of two numbers. be negative, their product, ab, will be negative, and the geometric mean will be the square root of a negative value, which is an imaginary number.

Is the geometric mean always less than the arithmetic mean?

The geometric mean is always lower than the arithmetic means due to the compounding effect. The arithmetic mean is always higher than the geometric mean as it is calculated as a simple average. It is applicable only to only a positive set of numbers. It can be calculated with both positive and negative sets of numbers.

Why arithmetic mean vs geometric mean?

The geometric mean differs from the arithmetic average, or arithmetic mean, in how it is calculated because it takes into account the compounding that occurs from period to period. Because of this, investors usually consider the geometric mean a more accurate measure of returns than the arithmetic mean.

What is the geometric mean between two numbers if A and B are negative?

if a and b are negative. (Definition 4 The geometric mean is the positive square root of the product of two numbers. (Definition 5) The geometric mean of two numbers, a and b, is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths a and b.

What is the geometric mean between two positive numbers m and n?

Property II: If A be the Arithmetic Means and G be the Geometric Means between two positive numbers m and n, then the quadratic equation whose roots are m, n is x^2 – 2Ax + G^2 = 0. Property III: If A be the Arithmetic Means and G be the Geometric Means between two positive numbers, then the numbers are A ± √A^2 – G^2.

Why is geometric mean more accurate?

The geometric mean takes into account the effect of compounding, therefore, better suited for calculating the returns. The use of Arithmetic means to provide more accurate results when the data sets are not skewed and not dependent on each other.