To find the Geometric Mean (G.M.) of a series of numbers, follow these steps:
1. List the numbers in the series.
The numbers given are:
[tex]\( 95, 70, 15, 75, 500, 8, 45, 250, 40, 36 \)[/tex]
2. Calculate the product of all the numbers in the series.
Compute the product of the numbers:
[tex]\( 95 \times 70 \times 15 \times 75 \times 500 \times 8 \times 45 \times 250 \times 40 \times 36 \)[/tex]
The product of these numbers is:
[tex]\( 484,785,000,000,000,000 \)[/tex]
3. Determine the number of elements in the series.
Count the numbers in the list:
The total number of elements is [tex]\( 10 \)[/tex].
4. Calculate the nth root of the product, where [tex]\( n \)[/tex] is the number of elements.
Here, [tex]\( n = 10 \)[/tex]:
The Geometric Mean (G.M.) is obtained by taking the 10th root of the product of the elements:
[tex]\( \sqrt[10]{484,785,000,000,000,000} \)[/tex]
5. Find the 10th root of the product.
Solving:
[tex]\( \sqrt[10]{484,785,000,000,000,000} \approx 58.68875779757121 \)[/tex]
Thus, the Geometric Mean (G.M.) of the given individual series is approximately [tex]\( 58.68875779757121 \)[/tex].
