Introduction to geometric mean statistics :

Geometric mean statistics is one of the forms in the mathematics. It is one of the type like mean or average, which indicates the innermost propensity or typical assessment of the set of numbers. It is much similar to arithmetic mean of the statistics, in which the most people think of with the word as "average", the given values are multiplied together and then finding the nth root for the total values. Here we are going to see about how to solve the geometric mean statistics and the sample problems and example problems related to it.
                                          

Definition of geometric mean statistics:

 

Geometric mean statistics is defined as, multiplying all the given values in the given data set, which is taken nth root for the total number of values multiplied. This is called as the geometric mean statistics.

Formula for measuring the geometric mean statistics,

Geometric mean = `root(n)(a_1xx a_2xx a_3xx a_4, .... xxa_n)`

 Where as,

`(a_1xx a_2xx a_3xx a_4, ....xx a_n)` is the total values in the data set.

n is the total number of values in the data set 

Procedure for solving geometric mean statistics:

  • Collect the total number of values in the given data set.
  • Multiply all the given values in the data set.
  • Then take the nth root for the multiplied values.

 

Geomettric mean statistics - Example problems:

 

Geometric mean statistics - Problem 1:

Find the geometric mean statistics for following data set 79, 62, 26, 49, 80, 95, 27.

Solution:

Geometric mean = `root(n)(a_1 xx a_2 xx a_3 xxa_4 ..... xxa_n)`

Here n = 7

= `root(7)(79 xx 62xx 26xx 49xx 80xx 95xx 27)`

= `root(7)(1280458670400)`

= `1280458670400^(1/7)`

 = 53.6566621

Therefore geometric mean statistics value for the  given data set is 53.6566661.

Geometric mean statistics - Problem 2:

Find the geometric mean statistics for following data set 68, 79, 92, 70, 45, 54, 67 and 90

Solution:

Geometric mean = `root(n)(a_1 xx a_2 xx a_3 xxa_4 ..... xxa_n)`

Here n = 8

= `root(8)(68 xx 79xx 92xx 70 xx 45 xx 54 xx 67 xx 90)`

= `root(8)(506927039472000)`

= `506927039472000^(1/8)`

 = 68.8839721

Therefore geometric mean statistics value for the  given data set is 68.8839721
                                           

Geomettric mean statistics - Practice problems:

 

Problem 1:

Find the geometric mean statistics for following data set .186, 133, 163, 184, 169, 155, 125, 145, and 175.

Answer: Therefore geometric mean statistics value for the  given data set is 158.080491.

Problem 2:

Find the geometric mean statistics for following data set .50, 75, 44, 32, 3, 29, 27, 55, 39, 10, and 13.

Answer:  Therefore geometric mean statistics value for the  given data set is 35.8004725