Geometric average

Definition

Geometric average is N times root in N variable value.

is divided into simple geometric average and weighted geometric average.

1, simple geometric average:

2, weighted geometric average:

Features

1, the geometric mean is affected by extreme values ​​than the arithmetic average;

2, if the variable value has a negative value, the calculated geometric average will become a negative number or Imaginary;

3, it is only suitable for data having an equal ratio or approximate, or an approximate ratio relationship;

4, the logarithm of geometric average is an arithmetic average of each variable value number.

Application

Example: Assuming a certain amount of savings (calculated by Deli): 5% lasts for 1.5 years, 3% lasts for 2.2%, lasts for 1 year. Ask the average savings year interest rate within 5 years.

Solution: By

to get the average savings year interest rate:

Geometric meaning

We know the arithmetic average,

makes a square shape, which is equal to a rectangle of a long width of A, B, which is a geometric average of the square of the square.

When the rectangular area mentioned in an ancient Chinese mathematics book is often represented by a long and wide geometric average.

Main use

Calculation geometric average requires connection between the various observations, and its main purpose is:

1, contrast ratio, index Wait average;

2, calculating average development speed;

wherein sample data is not negative, mainly for logarithmial distribution.

3, the average annual interest rate under Feeling;

4, the workshop of the continuous operation is average the average pass rate.

Knowledge Extension

Geometric average, square average number, adjustment average, arithmetic average size of size relationship:

reconciliation average ≤ geometric average Number ≤ arithmetic average ≤ square average number