If geometric mean of two numbers is 10 and one number is 5 the value of other number is

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Recall that in the proportion

a b = c d ,

b and c are called the means , and a and d are called the extremes .

When the means of a proportion are the same number, that number is called the geometric mean of the extremes.

So if

p x = x q ,

then cross-multiplying gives x 2 = p q . Taking the square root of both sides, we get x = p q as the geometric mean of p and q .

More generally, the geometric mean of a set of n numbers is the n th root of their product.

Example 1:

Find the geometric mean of 25 and 9

There are two numbers. So, the geometric mean of the two numbers is the square root of their product.

Geometric mean = 25 ⋅ 9

= 225 = 15

The geometric mean of 25 and 9 is 15 .

Example 2:

Find the geometric mean of 4 , 10 and 25 .

There are three numbers. So, the geometric mean of the three numbers is the cube root of their product.

Geometric mean = 4 ⋅ 10 ⋅ 25 3

= 1000 3 = 10

The geometric mean of 4 , 10 and 25 is 10 .

For geometric mean calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). For example: 853.4 709.0 457.7 980.3 -670.0 404.0 809.6 283.1 383.9 579.6 539.3 914.6 976.1

The geometric mean of the set of positive numbers is nth root of the product of the values (n=count of values). Similarity to the arithmetic average is after replace operators: sum by product and dividing by the n-th root.

Simple. First-type data elements (separated by spaces or commas, etc.), then type f: and further write frequency of each data item. Each element must have a defined frequency that count of numbers before and after symbol f: must be equal. For example:

1.1 2.5 3.99
f: 5 10 15

Grouped data are data formed by aggregating individual data into groups so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.

group	frequency
10-20	5
20-30	10
30-40	15

This grouped data you can enter:
10-20 20-30 30-40
f: 5 10 15Similar to a frequency table, but instead f: type cf: in the second line. For example:

10 20 30 40 50 60 70 80
cf: 5 13 20 32 60 80 90 100

The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. The last value will always be equal to the total for all observations since all frequencies will already have been added to the previous total.

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more math problems »

The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.

• First we multiply them: 2 × 18 = 36
• Then (as there are two numbers) take the square root: √36 = 6

In one line:

Geometric Mean of 2 and 18 = √(2 × 18) = 6

It is like the area is the same!

• First we multiply them: 10 × 51.2 × 8 = 4096
• Then (as there are three numbers) take the cube root: 3√4096 = 16

In one line:

Geometric Mean = 3√(10 × 51.2 × 8) = 16

It is like the volume is the same:

• First we multiply them: 1 × 3 × 9 × 27 × 81 = 59049
• Then (as there are 5 numbers) take the 5th root: 5√59049 = 9

In one line:

Geometric Mean = 5√(1 × 3 × 9 × 27 × 81) = 9

I can't show you a nice picture of this, but it is still true that:

1 × 3 × 9 × 27 × 81  =  9 × 9 × 9 × 9 × 9

Using scientific notation:

• A molecule of water (for example) is 0.275 × 10-9 m
• Mount Everest (for example) is 8.8 × 103 m

Geometric Mean= √(0.275 × 10-9 × 8.8 × 103)

 = √(2.42 × 10-6)

 ≈ 0.0016 m

Which is 1.6 millimeters, or about the thickness of a coin.

We could say, in a rough kind of way,

"a millimeter is half-way between a molecule and a mountain!"

Another cool one:

• A skin cell is about 3 × 10-8 m across
• The Earth's diameter is 1.3 × 107 m

Geometric Mean= √(3 × 10-8 × 1.3 × 107)

 = √(3.9 × 10-1)

 = √0.39

 ≈ 0.6 m

A child is about 0.6 m tall! So we could say, in a rough kind of way,

"A child is half-way between a cell and the Earth"

So the geometric mean gives us a way of finding a value in between widely different values.

Definition

For n numbers: multiply them all together and then take the nth root (written n√ )

More formally, the geometric mean of n numbers a1 to an is:

n√(a1 × a2 × ... × an)

Useful

The Geometric Mean is useful when we want to compare things with very different properties.

Example: you want to buy a new camera.

• One camera has a zoom of 200 and gets an 8 in reviews,
• The other has a zoom of 250 and gets a 6 in reviews.

Comparing using the usual arithmetic mean gives (200+8)/2 = 104 vs (250+6)/2 = 128. The zoom is such a big number that the user rating gets lost.

But the geometric means of the two cameras are:

• √(200 × 8) = 40
• √(250 × 6) = 38.7...

So, even though the zoom is 50 bigger, the lower user rating of 6 is still important.

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Copyright © 2022 Rod Pierce