Solving Geometric Means

Solving geometric means help to solve the data bounding many orders of intensity and for estimating ratios, percentages, other data sets covered by zero. Solving geometric means is defined for sets of positive correct numbers and determined by multiply all the numbers and taking the nth root of the whole. To find an average numbers presented as percentages we can use the geometric means solving method is used. Let us see about the formula for solving geometric means formula.

Formula for Solving Geometric Means:

Geometric Means:

Geometric Mean = ((X1) (X2) (X3)........ (XN))1/N
where

X = Individual score

N = Sample size (Number of scores)

Solving geometric means examples

1. Find the Geometric Mean of 1, 4, 6, 2, 5

Solution:Step 1: 4.932424

N = 5, the total number of values. Find `(1)/(N)`

`(1)/(N)`  = 0.2

Step 2:Now find Geometric Mean using the formula.

(1)(4)(6)(2)(5))0.2 = (240)0.2

So, Geometric Mean = 2.99255

2. Find the Geometric Mean of 16 & 5.

The geometric mean of 16 & 5 is

sq rt (16 * 5) = sq rt 80 = 8.94227

3. Find the Geometric Mean of 5, 10 and 15.

Solution:Step 1: N = 3, the total number of values. Find `(1)/(N)` .

`(1)/(N)`  = 0.3333.

Step 2: Now find Geometric Mean using the formula.

((5)(10)(15))0.3333 = (750)0.3333

So, Geometric Means of this numbers is = 9.0835.

4. Check the geometric means of these number is 4,5 and 6 is 4.20488.

Solution:Step 1:     4.932424

N = 3, the total number of values. Find `(1)/(N)`

`(1)/(N)`  = 0.3333.
Step 2:Now find Geometric Mean using the formula.

((4)(5)(6))0.3333 = (120)0.3333

So, Geometric Means of this numbers is = 4.932424.

Therefore 4.20488 is not the geometric means of 4, 5, and 6.

These are the examples of solving geometric means.

Practice problesm on solving geometric means

1. The geometric means of number 8, _, 4 is 5.76899. Find the missing number.

Ans: 6

2. Find the Geometric Mean of 1, 5, 12, 4, 8, 9.

Ans: 5.08460