Graphs – An Introduction
Slide 1
Graphs
An Introduction
This presentation is an introduction to
graphs and their uses
A graph is a visual representation of a
relationship between, but not restricted
to, two variables.
What is a graph?
 A graph is a visual representation of a relationship
between, but not restricted to, two variables.
 A graph generally takes the form of a one- or two-
Slide 2
dimensional figure. Although, there are threedimensional graphs available, they are usually
considered too complex to understand easily.
 A graph commonly consists of two axes called the x-axis
(horizontal) and y-axis (vertical).
 A graph can show Discrete or Continuous data types.
A graph generally takes the form of a
two-dimensional figure. Although, there
are three-dimensional graphs available,
they are usually considered too complex
to understand easily.
A graph commonly consists of two axes
called the x-axis (horizontal) and y-axis
(vertical).
Data types determines which graph to use.
There are two types of data that can be
shown by using a graph, Discrete and
Continuous
Discrete or Continous
Slide 3
Discrete:
Data that can be separated by some interval, for
example:
Recording the shoe sizes of a class – Bar graph
Continuous:
When data collected is continuous, for example:
Recording temperature – Line graph
There are two types of data that can be
shown by using a graph, Discrete and
Continuous.
To show continuous data effectively you
need to be able to join the points on the
graph, you would then be able to
interpolate the results of points not
recorded. Continuous data is usually
shown in the form of a line graph.
Discrete data is data that is discrete and
separate and can be counted, it is not
continuous. Discrete data is usually
shown by using a bar, column or
pictograph.
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Slide 4
20
Y – axis
This is a graph
25
Y – axis label
Scale or Increments
Graphs – An Introduction
10
All graphs (except Pie Chart) have common elements:
 Axis x and y (also z in 3D graphs)
 Axis labels
 A title
 Scales or Increments
 Can represent negative values
5
Origin – does not always have to start at 0,0
15
X-axis
-20
10
-10
-5
20
30
40
50
X-axis label
Scale or Increments
-10
A graph consists of basic elements.
ALL graphs should have a TITLE
All bar, line and scatter graphs should
have axis and axis labels
Scales are placed on the axis (they
resemble the markings on a ruler). On
the x-axis, to the right of the origin, the
numbers are positive and increase the
further they are away from the origin. On
the left of the origin the numbers are
negative, and decrease the further away
they are from the origin. Similarly on the
y-axis, above the origin the numbers are
positive and increase as they go up, the
numbers are negative below the origin
and decrease as they go lower.
The interval of the scale is the amount of
space along the axis from one mark to
the next. If the range of the scale is small,
the general rule is to take the range of
the scale and divide it by 10. Make this
your interval. For ranges that are larger,
the interval is typically 5, 10, 100, 500,
1,000, etc. Use numbers that divide
evenly into 100, 1,000 or their multiples
in order to provide a graph that is easy to
understand.
The origin of the X and Y axis do not have
to begin at the same number, and you do
not have to use the same scale, but the
values on the scale should remain the
same for that axis.
~2~
Graphs – An Introduction
25
and a horizontal line from
the y-axis
20
the point at which they meet
gives us the co-ordinate
15
Co-ordinates
Y – axis
If we draw a vertical line from
any point on the x-axis
A (3,15)
B (-4,10)
10
Slide 5
5
-5
-4
-3
-2
1
-1
2
3
-5
4
5
X-axis
-10
-15
C (-5,-15)
Back
If we draw a line from a point on the xaxis, either vertically up or down, and a
horizontal line, either left or right, from
the y-axis, the point at which they cross
gives us the co-ordinate of that point.
So, point A has a co-ordinate of 3,15
since the vertical line meets the x-axis at
3 and the horizontal line meets the y-axis
at 15
At point B, the vertical line meets the xaxis at -4 and the horizontal line meets
the y-axis at 10, therefore it’s coordinates are -4, 10
Similarly with point C, the co-ordinates
are both in the negative sector so it’s coordinates are -5, -15
Types of Graphs
Although these are the four basic types
of graphs, you should be aware that
there are many more specialised graph
types.
Four basic types of graph or chart
Line
Pie
Bar
Scatter
Slide 6
Creating a Line Graph
Line Graphs
A good method of showing the relationship between two variables
Slide 7
Pulse - Beats per minute
Exercise and Pulse Rate
200
150
Al a n - 28 yea r ol d
former a thl ete
100
A line graph is commonly used to show
the trend of data, such as temperature
over a period of time.
Ja net - 38 yea r ol d
s ecreta ry
50
0
0
30
60
90
120
Time in minutes
Back
~3~
Graphs – An Introduction
Bar graphs should be used when you are
showing segments of information.
A bar graph can have either horizontal or
vertical bars (Vertical bar graphs are
sometimes called Column charts). The
important point to note about bar graphs
is their bar length or height—the greater
their length or height, the greater their
value
When drawing bar graphs, draw a
vertical or horizontal bar for each
category. The height or length of the bar
will represent the value of the variable.
Select an arbitrary but consistent width
for each bar as well.
Bar Chart / Graph
Used to compare values in a category or between categories.
Slide 8
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The graph
shown here
makes a visual
comparison of
the fat content
of types of
cheese
Ed
am
Fat / 100g total
Fat content of cheeses
40
35
30
25
20
15
10
5
0
Cheeses
This graph has been turned on it’s side,
the information shown here could also
have been shown in the form of a line
graph.
It is important to look at the data before
deciding how to draw the graph, if the
number data on the x-axis is large, then
turn the paper to landscape format to
facilitate more increments.
Bar Chart / Graph
Can be useful to study trends over time
Daily Temperature Fluctuation
00:00
Time (24 hr)
20:00
Slide 9
16:00
12:00
08:00
04:00
00:00
-4
-2
0
2
4
6
8
10
12
Temperature (o C)
Creating a Bar Graph
Bar Chart / Graph
Multiple (or group) bar graphs compare relationships of
closely related sets
Slide 10
Back
Here groups of data have been used for
comparison. The y-axis label/ scale must
of course be common to all groups.
The double (or group) vertical bar graph
is a effective means of comparing sets of
data about the same places or items. This
type of vertical bar graph gives two or
more pieces of information for each item
on the x-axis instead of just one. This
allows you to make direct comparisons
on the same graph. However, if a group
vertical bar graph has too many sets of
data, the graph becomes cluttered and it
can be confusing to read.
~4~
Graphs – An Introduction
Creating Pie Charts
Pie Charts
A pie chart is used to show how a part of something relates to the
whole. This kind of graph is particularly suited to showing percentages
Slide 11
Red
7%
Pie charts are particularly useful to show
the percentage of sectors of a whole.
Survey of female hair colour
Multicoloured
7%
Blonde
47%
Brunette
39%
Back
Drawing a scatter graph is similar to
drawing a line graph in that co-ordinates
are used to plot the points. There are
usually more points to be plotted in a
scatter graph and the points can be in
groups, therefore it is not possible to
draw a line through all of the points.A
scatter graph shows how much
correlation there is between two
variables that you suspect may be linked
for instance height and weight as shown
here:
It is sometimes useful to draw a “line of
best fit” to show the trend
Slide 12
Drawing a scatter graph is
similar
to drawing
a line
A scatter
graph shows
graph
in that
co-ordinates
how much
correlation
are
used
to plot the
there
is between
two
points.
There
variables
that are
you usually
suspect
mayto
bebe
linked
for
more
points
plotted
height
andand the
ininstance
a scatter
graph
weight
as
shown
here:
points can be in groups,
therefore
it is not
possible
It is sometimes
useful
to
todraw
draw
a lineofthrough
all
a “line
best fit” to
the trend
ofshow
the points.
Weight (kg)
Scatter Graph
Line of best fit
Height (cm)
Back
A good graph:
Summary
A good graph:
Slide 13






Accurately shows the data
Grabs the reader's attention
Has a title and labels
Is simple and uncluttered
Clearly shows any trends or differences in the data
Is visually accurate (i.e., if one data value is 25 and another 50, then
50 should appear to be twice the size of 25).
•
•
•
•
•
Accurately shows the data
Grabs the reader's attention
Has a title and labels
Is simple and uncluttered
Clearly shows any trends or differences
in the data
• Is visually accurate (i.e., if one data value
is 25 and another 50, then 50 should
appear to be twice the size of 25).
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