SCATTER GRAPHS

A scatter graph compares two different measurements for a group of objects or

people.

Every point on the graph is a different object or person.

Scatter graphs are different to line graphs.

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.

Q1 Estimate the costs of the cheapest and the most expensive properties shown on the scatter graph.

Q2 How many bedrooms do these two properties have?

Q3 Is it fair to say that, for this sample, properties with more bedrooms are

usually more expensive? Is this always true?

100 200 300 400

1

2

3

4

Cost (£000)

Bedrooms

ANSWERS

Q1 Cheapest about £50 000; most expensive about £450 000.

Q2 One; four

Q3 Yes but not always true.

The X axis (horizonal) and the Y axis (vertical)

The next scatter graph has no numbers on the axes, but maybe if you “imagine”

them it will help you answer the question.

(the word “axes” is the plural of “axis” e.g. one axis, two axes)

“height” is being measured along the bottom line – the horizontal one - you’ll hear it

referred to as the X axis.

“age” is being measured up the side line – the vertical one - you’ll hear it referred to

as the Y axis.

76

Height

Age

54

3

21

The Bus Stop Queue

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

Write their names in the table.

Point 1 2 3 4 5 6 7

Person

GavinFredaErrolDennisCathyBrendaAlice

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 suggest 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 circle or a square,

we say there is zero correlation.

This 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.

For each of the following scatter graphs, decide whether they display

strong positive correlation

weak positive correlation

strong negative correlation

weak negative correlation

zero correlation

Q5 Q6

Q7 Q8

Q9

Premiership P

Goals conceded

Exam m

Shoe size

Rainf

Crop yield

Speed of

Amount of traffic

Cost of c

Cost of house

ANSWERSQ5 strong positive

Q6 weak negative

Q7 strong negative

Q8 weak positive

Q9 zero