BiVariate Data
edited version of ccollins @ www.lemars.k12.ia.us
When two pieces of data are collected
Data can be organized
as a SCATTERPLOT – if data is
numbers
Or
in a TWO WAY TABLE – if data is
categories
Scatter Plot
A scatter plot is a graph of a collection of ordered
pairs (x,y).
The graph looks like a group of dots, but some of
the graphs move in a general direction.
Positive Association
If the x-coordinates and the y-coordinates both
increase, then it is POSITIVE ASSOCIATION
This means that both values are going up
and a line of best fit can be drawn
Line of best fit shows the
general direction that a group
of points seems to be heading
Positive Association
If you look at the age of a child and the
child’s height, you will find that as the
child gets older, the child gets taller.
Because both are going up, it is
positive correlation.
Negative Association
If the y-coordinates decrease while the
x-coordinates increase then it is
NEGATIVE ASSOCIATION.
This means the two are related
as opposites and a line of
best fit can be drawn.
Negative Association
If you look at the age of your family’s car and its
value, you will find as the car gets older, the
car is worth less. This is negative association.
No Association
If there seems to be no
pattern, and the
points looked
scattered, then it is
no association.
This means the two are
not related.
No Association
If you look at the size shoe
a baseball player wears,
and their batting average,
you will find that the shoe
size does not make the
player better or worse,
then are not related.
Scatterplots
Which scatterplots below show a linear trend?
a)
c)
Negative
Association
e)
Positive
Association
b)
d)
f)
Constant
Association
Scatterplots
cluster – points are near
each other – not necessarily
any other correlation
cluster
outlier
outlier – when a point is
not near the line of best fit
non-linear association the
pattern of the points is
predictable, but not a line
linear association a line of
best fit can be drawn and
predictions can be made
non-linear
linear
Objective - To plot data points in the
coordinate plane and interpret scatter
plots.
y
Sport Utility Vehicles
(SUVs) Sales in U.S.
1991
1992
1993
1994
1995
1996
1997
1998
1999
0.9
1.1
1.4
1.6
1.7
2.1
2.4
2.7
3.2
Vehicle Sales (Millions)
Year Sales (in Millions)
5
4
3
2
1
1991 1993 1995 1997 1999
1992 1994 1996 1998 2000
Year
x
Scatterplot - a coordinate graph of data points.
y
Trend appears linear.
Year 
SUV Sales 
Positive association.
Predict the sales in 2001.
Vehicle Sales (Millions)
Trend is increasing.
5
4
3
2
1
1991 1993 1995 1997 1999
1992 1994 1996 1998 2000
Year
x
If bivariate data is about categories -not
numbers- it is displayed in a
Two Way Frequency Table
similar information to a venn diagram
21
22
70
30
100
Although all the information is not given,
using reason we can complete the table
A Relative Frequency Table
Shows the percent in each category –
Frequency can be compared to rows or
columns
you have to read carefully!!!
21
22
70
30
100
The relative frequency of cell phone owners who own a
mp3 player is…
you are comparing to mp3
cell phone
57
TOTAL mp3
70
= .81
21
22
70
30
100
what is the relative frequency
mp3
no mp3
total
cell phone
/70
/30
/100
no cell
/70
/30
/100
total
cell phone
no cell
total
mp3
57/70
13/70
70/70
no mp3
21/30
9/30
30/30
total
78/100
22/100
100/100
cell phone
no cell
total
mp3
.81
.19
1.00
no mp3
.70
.30
1.00
total
.78
.22
1.00