Bar Graphs 23/10/2015

Types of bar chart

Bar charts or bar graphs represent data as vertical blocks or columns.
The X axis shows what type of data each column represents, and the Y axis shows a value for that type of data. For example, in a rainfall graph, each column on the X axis represents a month of the year, with the height of each column on the Y axis showing the amount of rainfall in that month.

Compound

It is possible to split each column into sections to show the breakdown of data. For example, the employment data shown on the previous page could have been represented as three columns on a bar chart. The three columns would represent the three countries, with each column subdivided into sections showing primary, secondary and tertiary in different colours. This type of bar chart is sometimes called a compound bar chart.

Comparative

It is also possible to compare two sets of data on a bar chart - for example, measuring rainfall in two countries over the same period. This type of bar graph is called a comparative bar graph.
The chart below compares the tourism data for the UK in October 2001 with October the previous year. The graph shows how tourism declined after the terrorist attack in America in September 2001.

Bar chart showing decline in tourism to the UK

3D Shapes

3D solid shapes

Here are some common solid shapes.

Prisms and pyramids

A prism is a 3D shape which has a constant cross section - both ends of the solid are the same shape and anywhere you cut parallel to these ends will give you the same shape.

For example, in the prism below, the cross section is a hexagon.

This is called a hexagonal prism.

A pyramid has sloping faces that meet at a vertex.

Square-based pyramid

Tetrahedron

Drawing 3D shapes on isometric paper

You can use isometric paper to draw 3D shapes.

Remember to hold the isometric paper so that you can see vertical rows of dots!

This cube has been drawn using the dots as guides. The vertical lines are always vertical, but the horizontal lines are drawn at an angle, when drawn on isometric dotted paper. You could get some isometric paper and draw the cube yourself.

Perimeter 9th October Compund shapes

Compound shapes

Sometimes the shape is more complicated. In this case you need to calculate 'missing' lengths and be particularly careful to include all the sides.

Perimeter = 2 + 2 + 3 + 3 + 5 + 5 = 20 cm

Question

A plan of a play area is shown below:

Perimeter 9th october Simple shapes

Simple shapes

The perimeter of a shape is the length of its boundary.
Think of an ant starting from one corner of a small box, measuring 3 cm by 4cm. Imagine it walks all the way around the edge of the box. What distance will it have walked?

Perimeter = 4 + 3 + 4 + 3 = 14 cm

Straight Line Graphs 10th November 2015

When X= 0
Y is whatever the intercept of the line is.

The gradience tells us how much to go up in each time

Sometimes you are given a graph of a straight line and you need to find its gradient.
To find the gradient of a straight line:

• choose any two points on the line
• draw a right-angled triangle with the line as hypotenuse
• use the scale on each axis to find the triangle's:
  • vertical length
  • horizontal length
• work out the vertical length ÷ horizontal length
• the result is the gradient of the line

The following graph shows the exchange rate for euros € and United States dollars $ in March 2011.

There are two marked points at (0, 0) and (70, 98).
By working out the gradient of the graph, we can find the exchange rate from euros to United States dollars.

• The vertical distance between (0, 0) and (70, 98) is 98.
• The horizontal distance between (0, 0) and (70, 98) is 70.
• 98 ÷ 70 = 1.4

This means that 1 euro is equal to 1.4 United States dollars.