3.1 Understanding what graphs tell us

Mathematics

Grade 9

Number patterns, graphs, equasions,

Statistics and probability

Module 13

Understand what graphs tell us

Are graphs just pretty pictures?

ACTIVITY 1

To study a number of graphs with the aim of understanding what they can tell one

[LO 1.3, 5.5]

Graph A shows how the number of TV sets owned by every 1 000 people changed between 1985 and 1995 in six different regions in the world. For example, South Asia had 20 TV sets per 1 000 people in 1985, and 55 sets per 1 000 people in 1995.

Graph B shows, on the vertical axis, the number of people in prison in the United States of America in the years shown on the horizontal axis. For e x ample, in 1940 there were 135 000 people in prison.

• Work in pairs; one person works with graph A, answering question 1 below, and the other with Graph B and question 2. Give the reason or explanation for each of your answers.

1 Study graph A , then write down answers and explanations to these questions:

1.1 Which region had the smallest number of TV sets per 1 000 in 1985?

1.2 Which region had the highest number of TV sets per 1 000 in 1995?

1.3 In which region did the number of TV sets per 1 000 increase the most?

1.4 Is there a region where the number of TV sets per 1 000 has decreased?

1.5 Compare Sub–Saharan Africa with the Arab States and discuss the change in the number of TV sets per 1 000 in these two regions.

1.6 Draw a similar graph showing two other regions: South Africa and the United States of America. Make up the figures.

2 Now study graph B and answer these questions:

2.1 From the graph, try to estimate how many people were in prison in these years:

a) 1930 b) 1950 c) 1995

2.2 In 1980, were there more than or fewer than 200 000 people in jail?

2.3 There is a dip in the graph just after 1940. What do you think the graph is telling us?

2.4 Say roughly how many years it took for the prison population to double from what it was in 1950

2.5 How long did it take the prison population to double from what it was in 1985?

2.6 Would you say that the number of people in jail in the USA keeps increasing? Give reasons.

2.7 From the information in the graph make a prediction about the number of people in USA jails in the future.

3 In Geography, an interesting kind of graph is a section drawing. This shows how the height of the land varies over a straight line between two places. Here is one for the line between Bottelaryberg and Papegaaiberg, two hills near Stellenbosch. All the measurements are in metres. From this we can see (on the left) that Bottelaryberg is about 470 m above sea level, and Papegaaiberg about 255 m above sea level. Walking in a straight line from Bottelaryberg you come to sharp dip, after about 2,5 km, and then, for the next half a kilometre, you go over a little rounded rise.

• This is a very useful graph for road planners, as it shows the steepness of the terrain.

  

• We can clearly see that the descent from the top of Bottelaryberg is very steep, as the line drops sharply over about 750 m. But, if you were on top of Papegaaiberg, and going down in the direction of Bottelaryberg, it would take 1,5 km to drop the same distance, making the route much less steep.