1 lesson 6.2.3 using scatterplots. 2 lesson 6.2.3 using scatterplots california standards:...
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Lesson 6.2.3Lesson 6.2.3
Using ScatterplotsUsing Scatterplots
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Lesson
6.2.3Using ScatterplotsUsing Scatterplots
California Standards: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).
Mathematical Reasoning 2.3Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
What it means for you:You’ll predict data values using scatterplots. You’ll also practice finding the highest and lowest values in a data set.
Key words:• prediction• scatterplot• line of best fit
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Using ScatterplotsUsing ScatterplotsLesson
6.2.3
If you have many pairs of values plotted on a scatterplot, and they all fall in a neat band, you know the two variables are correlated.
If you plotted some more pairs of values, you’d expect them to lie within the band of points. You can use this idea to predict values.
For instance, from the scatterplot of ice cream sales against average temperature, you could predict how many ice creams would be sold when the temperature was 50 °F.
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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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Using ScatterplotsUsing Scatterplots
Finding the Highest and Lowest Values
Lesson
6.2.3
Box-and-whisker plots don’t show all the raw values — just the maximum and minimum values and the general trends.
Scatterplots are different — they show the raw data values, as well as trends.
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Using ScatterplotsUsing Scatterplots
Example 1
Solution follows…
Lesson
6.2.3
The scatterplot below shows the number of burglaries per 1000 people against the percentage of households that have burglar alarms installed. What was the greatest number of burglaries per 1000 people recorded?
% of households with burglar alarms
No.
of
burg
larie
s pe
r 10
00 p
eopl
e
Solution
The highest number of burglaries recorded per 1000 people is 60.
The greatest number of burglaries recorded is the point that lies furthest up the vertical axis on the graph.
0 20 40 60 80 100
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60
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100
0
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Using ScatterplotsUsing Scatterplots
Guided Practice
Solution follows…
Lesson
6.2.3
For Exercises 1–3, refer to the scatterplot on the right.
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40
60
80
100
0
Amount of gasoline sold on street B per day ($)
No
. of c
ars
usi
ng
st
ree
t A p
er d
ay
1. What was the highest number of cars recorded using street A on a single day?
2. What was the greatest amount of money spent on gasoline in street B on any day?
3. How many cars used street A on the day when the least amount of gasoline was sold on street B?
86
$91
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Using ScatterplotsUsing Scatterplots
For Exercises 1–3, refer to the scatterplot on the right.
1. What was the highest number of cars recorded using street A on a single day?
2. What was the greatest amount of money spent on gasoline in street B on any day?
3. How many cars used street A on the day when the least amount of gasoline was sold on street B?
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Using ScatterplotsUsing Scatterplots
A Line of Best Fit Shows the Trend in the Data
Lesson
6.2.3
Not many sets of data are perfectly correlated, so a line of best fit is used to show the trend.
If the data was perfectly correlated you’d expect all the points to lie on this line.
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Using ScatterplotsUsing Scatterplots
Example 2
Solution follows…
Lesson
6.2.3
Draw a line of best fit on the scatterplot below.
% of households with burglar alarms
No.
of
burg
larie
s pe
r 10
00 p
eopl
e
0 20 40 60 80 100
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80
100
0The line of best fit splits the data approximately in half. You should have roughly the same number of points on each side of the line.
Solution
The scatterplot shows negative correlation, so the line of best fit will have a negative slope.
About half the data points are on this side of the line…
…and about half the data points are on this side of the line.
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Using ScatterplotsUsing Scatterplots
Guided Practice
Solution follows…
Lesson
6.2.3
4. The hand spans of 11 students are measured, together with the lengths of their arms. The measurements are recorded in the table below.
Hand span (cm)
Arm length (cm)
19
50
18
46
20
56
15
40
21
60
22
63 48 44
16 17
48 57 60
20 24 26
Plot a scatterplot of this data. Add a line of best fit to your scatterplot.
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10 15 20 25Hand span (cm)
Arm
len
gth
(cm
)30
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Using ScatterplotsUsing Scatterplots
Guided Practice
Solution follows…
Lesson
6.2.3
5. The ages and values of a particular type of car are recorded on the right.
Age of car (years) Value of car ($)
0 10,000
2 9000
7 4000
12 1000
11 4000
6 6000
7000
8000
8
1
7000
6000
8000
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3
3
50008
40009
10
8
6
4
2
0 4 6 8 10Age of car (years)
Val
ue
of
car
($10
00)
2 120
Plot a scatterplot of this data. Add a line of best fit to your scatterplot.
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Using ScatterplotsUsing Scatterplots
Use Lines of Best Fit to Make Predictions
Lesson
6.2.3
If there is a correlation, you can use a line of best fit to predict what other data points might be.
You can’t add a line of best fit to data that has no correlation.
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Using ScatterplotsUsing Scatterplots
Example 3
Solution follows…
Lesson
6.2.3
Predict the number of burglaries per 1000 people if 50% of households have burglar alarms.
Solution
% of households with burglar alarms
No.
of
burg
larie
s pe
r 10
00 p
eopl
e
0 20 40 60 80 100
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100
0
When 50% of households have burglar alarms, the number of burgaries per 1000 people is expected to be around 33.
Start at 50% on the horizontal axis.
Read across from the line of best fit to the vertical axis.
Read up to the line of best fit.
50
33
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Using ScatterplotsUsing Scatterplots
Guided Practice
Solution follows…
Lesson
6.2.3
In Guided Practice Exercise 4, you drew a scatterplot of arm length against hand span.
Use your line of best fit to predict:
6. the arm length of a student with a 23 cm hand span.
7. the hand span of a student with a 52 cm arm length.
about 60 cm
about 20 cm
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55
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10 15 20 25Hand span (cm)
Arm
len
gth
(cm
)
30
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Using ScatterplotsUsing Scatterplots
Guided Practice
Solution follows…
Lesson
6.2.3
In Guided Practice Exercise 5, you drew a scatterplot of values against ages for a certain type of car.
Use your line of best fit to predict:
8. the expected value of a 5-year-old car of this type.
9. the age of a car that is valued at $5500.
about $7000
about 7 years old
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8
6
4
2
0 4 6 8 10Age of car (years)
Val
ue
of
car
($10
00)
2 120
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Using ScatterplotsUsing Scatterplots
Independent Practice
Solution follows…
Lesson
6.2.3
The table below shows the height (in feet) of mountains with their cumulative snowfall on April 1st (in inches).
1. Create a scatterplot of the data.
2. Draw in a line of best fit for the data.
3. A mountain has a height of 7200 feet. What would you expect its cumulative snowfall to be on April 1st?
153 174
6700 7900
249 172 128
7600 6800 6200Height (ft)
Snowfall (in) 32
5800
238
8200
162
6700
about 200 inches
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05 6 7 8 9Height (1000 ft)
Sn
ow
fall
(in
)
50
250
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Using ScatterplotsUsing Scatterplots
Round UpRound Up
Lesson
6.2.3
Lines of best fit follow the trend for the data.
You can use them to predict values — but remember, chances are your predictions won’t be totally accurate.
They can give you a good idea though.