Geometric Mean

                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.

Example: What is the Geometric Mean of 2 and 18?

• 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!

Example: What is the Geometric Mean of 10, 51.2 and 8?

• 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:

MEAN MACHINE

The Mean Machine

See how the Arithmetic Mean (or Average) is calculated:

To find the Mean (or Average) divide the
Sum of the numbers by the Count of the numbers

 Numbers: 

7

7

21

7

= 3

 Count

 Sum

 Count

Divide

© 2016 MathsIsFun.com v0.61

How to Find the Mean

The mean is the average of the numbers.

It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

In other words it is the sum divided by the count.

Example 1: What is the Mean of these numbers?

6, 11, 7

• Add the numbers: 6 + 11 + 7 = 24
• Divide by how many numbers (there are 3 numbers): 24 / 3 = 8

The Mean is 8

Histograms

Histogram: a graphical display of data using bars of different heights.

It is similar to a Bar Chart, but a histogram groups numbers into ranges .

The height of each bar shows how many fall into each range.

And you decide what ranges to use!

DIFFERENCE BETWEEN BAR GRAPH AND HISTOGRAM:

BAR GRAPH

Bar Graphs

A Bar Graph (also called Bar Chart) is a graphical display of data using bars of different heights.

Imagine you just did a survey of your friends to find which kind of movie they liked best:

Table: Favorite Type of Movie
Comedy	Action	Romance	Drama	SciFi
4	5	6	1	4

We can show that on a bar graph like this:

                It is a really good way to show relative sizes: we can see which types of movie are most liked, and which are least liked, at a glance.

               We can use bar graphs to show the relative sizes of many things, such as what type of car people have, how many customers a shop has on different days and so on.

DATA

What is Data?

Data is a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things.

Qualitative vs Quantitative

Data can be qualitative or quantitative.

• Qualitative data is descriptive information (it describes something)
• Quantitative data is numerical information (numbers)

Quantitative data can be Discrete or Continuous:

• Discrete data can only take certain values (like whole numbers)
• Continuous data can take any value (within a range)

More Examples

Qualitative:

• Your friends' favorite holiday destination
• The most common given names in your town
• How people describe the smell of a new perfume

Quantitative:

• Height (Continuous)
• Weight (Continuous)
• Petals on a flower (Discrete)
• Customers in a shop (Discrete)

Surds

When we can't simplify a number to remove a square root (or cube root etc) then it is a surd.

Example: √2 (square root of 2) can't be simplified further so it is a surd

Example: √4 (square root of 4) can be simplified (to 2), so it is not a surd!

Have a look at some more examples:

Number	Simplified	As a Decimal	Surd or not?
√2	√2	1.4142135...(etc)	Surd
√3	√3	1.7320508...(etc)	Surd
√4	2	2	Not a surd
√¼	½	0.5	Not a surd
3√11	3√11	2.2239800...(etc)	Surd
3√27	3	3	Not a surd
5√3	5√3	1.2457309...(etc)	Surd

The surds have a decimal which goes on forever without repeating, and are Irrational Numbers.

ALGEBRA - EQUATION AND FORMULA

Equations and Formulas

What is an Equation?

An equation says that two things are equal. It will have an equals sign "=" like this:

x

+

2

=

6

That equations says: what is on the left (x + 2) is equal to what is on the right (6)

So an equation is like a statement "this equals that"

(Note: this equation has the solution x=4)

What is a Formula?

A formula is a fact or rule that uses mathematical symbols.

It will usually have:

• an equals sign (=)
• two or more variables (x, y, etc) that stand in for values we don't know yet