Can arithmetic mean and geometric mean be same?

The case where all the terms are equal then their sum is nx1, so their arithmetic mean is x1; and their product is x1n, so their geometric mean is x1; therefore, the arithmetic mean and geometric mean are equal, as desired.

What is the main key difference between arithmetic mean and 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.

When we use arithmetic mean geometric mean and harmonic mean?

The arithmetic mean is appropriate if the values have the same units, whereas the geometric mean is appropriate if the values have differing units. The harmonic mean is appropriate if the data values are ratios of two variables with different measures, called rates.

How do you find the arithmetic mean geometric mean and harmonic mean?

Harmonic mean is a type of average that is calculated by dividing the number of values in a data series by the sum of the reciprocals (1/x_i) of each value in the data series. A harmonic mean is one of the three Pythagorean means (the other two are arithmetic mean and geometric mean. It is the average return).

How do you evaluate an elliptic integral?

Steps

1. Set up the integral to be evaluated.
2. Write the integral in terms of the binomial series.
3. Evaluate the integral using the Beta function.
4. Use Euler’s reflection identity and the fact that Γ ( 1 / 2 ) = π {\displaystyle \Gamma (1/2)={\sqrt {\pi }}} .
5. Use the double factorial identity.
6. Expand the series.

When should we use geometric mean instead of arithmetic mean?

The arithmetic mean is more useful and accurate when it is used to calculate the average of a data set where numbers are not skewed and not dependent on each other. However, in the scenario where there is a lot of volatility in a data set, a geometric mean is more effective and more accurate.

How do you tell the difference between arithmetic and geometric?

An arithmetic sequence is a sequence of numbers that is calculated by subtracting or adding a fixed term to/from the previous term. However, a geometric sequence is a sequence of numbers where each new number is calculated by multiplying the previous number by a fixed and non-zero number.

What is an elliptic integral?

Elliptic Integral. An elliptic integral is an Integral of the form. or. where , , , and are Polynomials in and is a Polynomial of degree 3 or 4. Another form is. where is a Rational Function of and , is a function of Cubic or Quadratic in , contains at least one Odd Power of , and has no repeated factors.

What is the use of arithmetic and geometric mean?

The arithmetic–geometric mean can be used to compute – among others – logarithms, complete and incomplete elliptic integrals of the first and second kind, and Jacobi elliptic functions. From the inequality of arithmetic and geometric means we can conclude that:

What is the elliptic function?

Elliptic Functions (among which the Jacobi Elliptic Functions and Weierstraß Elliptic Function are the two most common forms) provide a powerful tool for analyzing many deep problems in Number Theory , as well as other areas of mathematics. All elliptic integrals can be written in terms of three “standard” types. To see this, write

What is the arithmetic mean of X and Y?

In mathematics, the arithmetic–geometric mean ( AGM) of two positive real numbers x and y is defined as follows: These two sequences converge to the same number, the arithmetic–geometric mean of x and y; it is denoted by M(x, y), or sometimes by agm (x, y) .