Graphs Comparing Quantities

breakeven_graph.jpgSeveral types of graphs are studied at this level.

There are:

  • Rate of change graphs
  • Coordinate x-y graphs
  • Statistical graphs

e.g Distance / time 
e.g. Linear quadratic functions 
e.g. Bar graphs and pie charts

Most graphs involve a horizontal axis and a vertical axis.

All graphs should have a title, labelled axes with the scale and units clearly indicated.

Rates of Change

A rate compares two quantities of a different kind. Because two quantities are being compared, a graph with two axes is a convenient way to illustrate this.

e.g. Speed = kilometre per hour Y9_Graphs_Comparing_Quantities_01.gif.

The graph below shows the distance travelled by a cyclist on a journey over a period of 10 hours.

Y9_Graphs_Comparing_Quantities_02.gif

Y9_Graphs_Comparing_Quantities_03.gif

 

 

The graph shows:

For the first two hours the cyclist travels 50 km
i.e. Average speed of 50/2 = 25 km/h

For the next hour the cyclist is resting.

For the next hour the cyclist travels 25 km
i.e. Average speed of 25/1 = 25 km/ h

For the next hour the cyclist is resting.

For the next 5 hours the cyclist covers 175 km
i.e. Average speed 0f 175/5 = 35 km /h

For the whole journey, the cyclist covers 250 km in 10 hours for an average speed of 250/10 = 25 km/h

 

Notice that time is usually on the horizontal axis in this type of graph and that the steeper the graph (i.e. the bigger the gradient) the greater the speed (i.e. the quicker the cyclist is travelling.)

Comparison Graphs

A scatter graph is a useful way to compare two quantities to see if there is a relationship between them.

Example

Compare the heights and weights of the following six people and see if there is a connection between their heights and weights.

Name
Weight(kg)

Height(cm)
Elizabeth
49
150
Porewa
38
135
Ruan
59
165
Jimmy
55
155
Irina
43
145
Sam
62
175

Y9_Graphs_Comparing_Quantities_04.gif

A zig-zag line could be put at the beginning of the height axis to show it does not start at 0.

From the graph, there would appear to be a connection between height and weight.

The heavier the person the taller they are.

Remember this is only for these six people and may not be true for a larger group or for people in general. 
What do you think?