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

                 WILLIAM  TIMOTHY  GOWERS

                              Sir William Timothy Gowers, FRS (born 20 November 1963) is a British mathematician. He is a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, where he also holds the Rouse Ball chair, and is a Fellow of Trinity College, Cambridge. In 1998, he received the Fields Medal for research connecting the fields of functional analysis and combinatorics.
  
                             Gowers has written several works popularising mathematics, including
 Mathematics: A Very Short Introduction (2002), which describes modern mathematical research for the general reader. He was consulted about the 2005 film Proof, starring Gwyneth Paltrow and Anthony Hopkins. He edited The Princeton Companion to Mathematics (2008), which traces the development of various branches and concepts of modern mathematics. For his work on this book, he won the 2011 Euler Book Prize of the Mathematical Association of America.