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Lesson 6.2.2Lesson 6.2.2
Shapes of ScatterplotsShapes of Scatterplots
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Lesson
6.2.2Shapes of ScatterplotsShapes of Scatterplots
California Standard:Statistics, Data Analysis, and Probability 1.2Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).
What it means for you:You’ll learn about different types of correlation and what they look like on scatterplots.
Key words:• slope• positive correlation• negative correlation• strong correlation
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Shapes of ScatterplotsShapes of ScatterplotsLesson
6.2.2
In the last Lesson, you learned how to make scatterplots from sets of data.
By looking at the pattern of the points in a scatterplot, you can decide how the variables are related — for example, whether ice cream sales really do increase on hot days.
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Shapes of ScatterplotsShapes of Scatterplots
Positive Slope Means Positive Correlation
Lesson
6.2.2
If two things are correlated, they are related to each other — if one changes, the other will too.
Two variables are positively correlated if one variable increases when the other does. For example, children’s heights are positively correlated with their ages — because older children are typically taller than younger ones.
Variables are positively correlated if one variable increases as the other does.
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Shapes of ScatterplotsShapes of Scatterplots
If two positively correlated variables are plotted on a scatterplot, the points will lie in a band from bottom left to top right. If you were to draw a line through the points it would have a positive slope.
Lesson
6.2.2
The thinner the band of points on the scatterplot, the more strongly correlated the data is.
This graph shows positive correlation.
This graph shows strong positive correlation.
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Shapes of ScatterplotsShapes of Scatterplots
Negative Slope Means Negative Correlation
Lesson
6.2.2
Negative correlation is when one quantity increases as another decreases. For example, values of cars usually decrease as their age increases.
Variables are negatively correlated if one variable increases as the other decreases.
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Shapes of ScatterplotsShapes of ScatterplotsLesson
6.2.2
The thinner the band of points, the more strongly correlated the data is.
This graph shows negative correlation.
This graph shows strong negative correlation.
If a scatterplot shows negative correlation, the points will lie in a band from top left to bottom right. They’ll follow a line with a negative slope.
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Shapes of ScatterplotsShapes of Scatterplots
No Obvious Correlation Means Random Distribution
Lesson
6.2.2
When points seem to be spread randomly all over the scatterplot, then it is said that there is no obvious correlation.
For example, people’s heights and their test scores are not correlated — the height of a person has no effect on their expected test score.
This graph shows no obvious correlation.
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Shapes of ScatterplotsShapes of Scatterplots
Example 1
Solution follows…
Lesson
6.2.2
Describe the correlation shown in the scatterplot opposite.
Solution
The correlation is fairly strong — the points lie in a fairly narrow band.
The plot shows positive correlation. (As the temperature increases, the number of ice creams sold tends to increase.)
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040 9050 60 70 80
Temperature (°F)
Num
ber
of ic
e cr
eam
s so
ld
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Shapes of ScatterplotsShapes of ScatterplotsLesson
6.2.2
If it was perfect the points would lie in a straight line, as shown on the left.
The correlation in Example 1 is strong, but it isn’t perfect.
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040 9050 60 70 80
Temperature (°F)
Num
ber
of ic
e cr
eam
s so
ld
180
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80
40
040 9050 60 70 80
Temperature (°F)
Num
ber
of ic
e cr
eam
s so
ld
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Shapes of ScatterplotsShapes of Scatterplots
Guided Practice
Solution follows…
Lesson
6.2.2
In Exercises 1–2, describe the type of correlation.
1. 2.
0 20 40 60 80 100
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40
60
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100
0
% of households with burglar alarms
No
. of b
urg
lari
es
per
10
00 p
eo
ple
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100
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Amount of gasoline sold on street B per day ($)
No
. of c
ars
usi
ng
st
ree
t A p
er d
ay
negative no correlation
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Shapes of ScatterplotsShapes of Scatterplots
Guided Practice
Solution follows…
Lesson
6.2.2
In Exercises 3–4, describe the type of correlation.
3. 4.
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100
Average test score (%)
Atte
nda
nce
(%
) 90
0 2 4 6 8 10
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2
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0
Grade levelT
ime
sp
ent o
n
hom
ew
ork
per
day
(h
)positive strong positive
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Shapes of ScatterplotsShapes of Scatterplots
Independent Practice
Solution follows…
Lesson
6.2.2
1. Brandon investigates the relationship between the number of spectators at a football game and the amount of money taken at the concession stand. What kind of correlation would you expect?
2. If every job you do takes one job off your to-do list, what kind of correlation would you expect between the number of jobs you do and the number of jobs on your to-do list?
positive
negative
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Shapes of ScatterplotsShapes of Scatterplots
Independent Practice
Solution follows…
Lesson
6.2.2
In Exercises 3–4, describe the correlation shown.
3. 4.
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End of year test scoreN
o. o
f da
ys a
bse
nt
fro
m s
choo
lperfect positive correlation weak negative correlation
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Length of square (in)
Wid
th o
f sq
uar
e (
in)
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Shapes of ScatterplotsShapes of ScatterplotsLesson
6.2.2
Round UpRound Up
If the points lie roughly in a diagonal line across a scatterplot, it means the variables are correlated.
An “uphill” band means positive correlation, whereas a “downhill” band means negative correlation.
Positive correlation
Negative correlation
