SCATTER GRAPHS

A scatter graph will have a horizontal axis and a vertical axis like a line graph but

scatter graphs are different to line graphs (and used for different things). You plot

points on both but on a line graph you can join the points up to get a line (if you want,

you don’t have to, you can just leave them as points).

You don’t join the points up in a scatter graph.

In a line graph the points relate to a SINGLE object or person. Examples would be

a patient’s temperature changing over time

patient’s temperature (vertical axis) vs time (horizontal axis)

the depth of the water in a harbour as the tide goes in and out

depth (vertical axis) vs time (horizontal axis)

how fuel efficient a car engine is at different speeds

fuel consumption (vertical axis) vs speed (horizontal axis)

In a scatter graph you are looking at MANY things. Every point on the graph is a

different object or person. Each point plotted will use two measurement relating to

that one object or person.

If a scatter graph is being used it’s because someone is trying to see if the two

measurements are linked in some way. They’re looking to see if there is some rela-

tionship between the values. This is called a correlation.

SUMMARY

You don’t join the points up in a scatter graph.

A line graph has points relating to a SINGLE object or person. You can join

them up with a line.

A scatter graph has points where each point is a DIFFERENT object or per-

son. You don’t join the points up.

Here is some information about properties for sale in Perth (each dot is a different

house or flat). The scatter graph compares the asking price of each property with

the number of bedrooms.

100 200 300 400

1

2

3

4

Cost (£000)

Bedrooms

Look at the scatter graph and answer these questions.

Q1 Estimate the cost of the cheapest property shown on the scatter graph.

Q2 How many bedrooms does this property have?

Q3 Estimate the cost of the most expensive property.

Q4 How many bedrooms does this property have?

Q5 Is it fair to say that, for this sample, properties with more bedrooms are

usually more expensive?

Q6 Is this always true?

ANSWERS

Q1 Cheapest about £50 000

Q2 One

Q3 Most expensive about £450 000.

Q4 Four

Q5 Yes

Q6 Not always true

e.g. there’s a two bedroom which costs more the three bedrooms

The next scatter graph has no numbers on either axis.

(If you imagine them it will help you answer the question).

HEIGHT is on the horizontal axis (you might hear it called the X axis).

AGE is on the vertical axis (you might hear it called the Y axis).

Q4 Who is represented by each point on the scatter graph?

Write their names in the table.

Point 1 2 3 4 5 6 7

Person

ANSWERS

Point 1 2 3 4 5 6 7

Person Dennis Alice Freda Brenda Errol Cathy Gavin

Scatter graphs and CORRELATION

A scatter graph can help give an indication of whether there is relationship between

the two measurements. The technical word for this relationship is correlation.

Students study correlation in courses like Social Science and Business Statistics.

In the first scatter graph there was definitely a connection between property prices

and the number of bedrooms. As one figure goes up, so does the other. That’s

called a positive correlation.

What does a positive correlation look like?

If there is a positive correlation between the two measurements, the points will lie

something like this:

The basic group (the oval surrounding the points) slopes upwards to the right.

Examples of measurements which would have a positive correlation:

Children’s age and height

Children’s age and shoe size

Height and shoe size (taller people tend to have bigger feet)

Height and weight (taller people tend to be heavier)

What does a negative correlation look like?

If there is a negative correlation between the two measurements, the points will lie

something like this:

As one measurement goes up, the other goes down.

Examples of measurements which would have a negative correlation:

The older a man gets, the less hair he has

As temperature decreases, more heaters are purchased (sales of portable

heaters go up when it gets colder)

The more someone works, the less free time they have

There may not be a correlation.

If the points are evenly spread throughout a circle or a square,

we say there is zero correlation.

This next scatter graph shows a very strong positive correlation.

The surrounding oval is very narrow.

At its most extreme, if the points made a perfect straight line you would have the

strongest possible correlation.

Try this online test to see if you can spot the scatter graphs with a correlation.