Download Data Analysis

PERIOD
DATE
Lesson
t Retearh
Scafter Plots
A scatter plot shows the relationship between a data set with two variables graphed as ordered pairs.
The pattern of the data points determines the association between the two sets of data.
. Data points that go generally upward from Ieft to right show a positive association.
. Data points that go generally downward from left to right show a negative association.
. Data points with no clear pattern show no association between the data sets.
Examples
Explain whether the scatter plot of the
data shows a positiue, negatiae, ot no
association. Interpret the scatter plot.
-to
q,u
36
1. miles driven and gallons of gas used
o
24
€
As the number of miles driven increases, the amount of gas
used increases. Therefore, the scatter plot will show a
positive association. There appears to be a linear association.
3z
0
50
100
150
illihs Driven
2. number of minutes a candle burns and a
candle's height
c
vt)
ll)
-,c
As the number of minutes increases, the height of the candle
will decrease. Therefore, the scatter plot will show a negative
association. There appears to be a linear association.
E
e
=1
!a
e)
0
Exercises
Explain whether the scatter plot of the data for each of the
following shows a positive, negatiae, or no association.
Interpret the scatter plot.
2.^
1.
3.
9
Eoo
G
6Q
E
s7
!o
.9
E
GA
o
.H
o
€40
30
o
Ee
'E
izo
'9
z
tL5
o
-4
o
6=5
4
o
!o
o
Ero
-20
z2
o
I
I
5I01520
'
I
246
=
Age (years)
F
o
Coutse 3
.
Chapter
9
Scatter Plots and Data Analysis
Shower Time (minutes)
1234567
Day ol the Week
I29
NAME
PERIOD
DATE
Lesson 2 Reteath
lines of Best Fit
Examples
BOATS Boat sales at Dustin's Marina are given.
Week
Boat Sales
1.
1
2
.)
4
5
6
7
8
2
3
t)
8
6
10
8
18
Construct a scatter plot using the data. Then draw
and assess a Iine that seems to best represent
the data.
Graph each of the data points. Draw a line
that fits the data.
I8
I6
,tr
14
t.
o
Ero
E8
a!
q,
6
Use the line of best frt to make a conjecture about
boat sales in week 9.
Extend the line so that you can estimate the y-value
for an r-value of 9. The y-value for the 9th week is
16 boats. We can predict that Dustin's Marina will
sell 16 boats in week 9.
4
2
o123456
Week
Exercises
1. OUTDOOR CLUB The table shows the number of new
members to join the Outdoor Club.
E
I
Day
New Members
!
1
2
.)
4
5
6
3
6
4
3
6
4
9
8
_7
36
sl
Construct a scatter plot ofthe data. Then draw and
assess a line that seems to best represent the data.
=74
q
z3
2
1
b. Use the line of best frt to make a conjecture about the
number of new members to join the club on the eighth
o
day.
-o
c
E
2.
PORTFOLTO The table shows the value of Heather's
portfolio, in thousands of dollars, at the end of
a90
€so
o
each year.
=i
!
g
B- oo
Year
Value
E
F
o
'=
Ezo
1
2
3
4
5
6
?to
90
70
80
60
80
60
340
a. Construct a scatter plot ofthe data. Then draw and
assess a line that seems to best represent the data.
b. Use the line of best frt to make
a conjecture about the
value of Heather's portfolio at the end of year 8.
Course
I . Chapter 9 Scatter Plots and Data Analysis
.9
30
Ero
tro
0 I25
456789
Year
lrt
NAME
PERIOD
DATE
Lesson 5 Reteach
Two-Way Thbles
Erample t
Marisa surveyed students at her school. She found that 30 out of 75 seventh
gladers buy their lunch. There are 25 out of 76 eighth graders who do not buy
their lunch. Construct a two-way table summarizing the data.
Step I Create a table using the trvo-categories: buy lunch and grade level. Fill in the table
with the given values.
Step 2 IJse reasoning to complete the table, Remember, the totals are for each row and
column. The column labeled "Total" should have the same sum as the row labeled
"Total."
Seventh Graders
Eighth Graders
TotaI
Buy Lunch
Do Not Buy Lunch
Total
30
45
75
51
25
76
81
70
151
Example 2
Find and interpret the relative ftequencies of seventh graders in the survey from
Example I by row. Bound to the nearest hundredth if necessary.
Buy Lunch
E
e
Seventh Graders
Bo;;$
:
Eighth Graders
ur,#
= 0.67
Total
.9
o.4o
B1
Do Not Buy Lunch
Total
45;#:0.60
75;#:1.00
25;#=
za,ff=
70
0.33
1.oo
151
Sample answer: Less than half of the seventh graders and more than half of the eighth
graders buy their lunch.
-o
Exercise
Find and interpret the relative frequencies of seventh gladers in the survey from
Example 1 by column. Round to the nearest hundredth if necessary.
i
E
F
Course 5
.
Chapter
9
Scatter Plots and Data Analysis
I55
PERIOD
DATE
lesson 4 Reteath
D esc ri pff
ve Sta tfstics
Example t
Find the ill€anr median, rnode, and range of the data
showu in the table.
Mean
80 88 81
92 88 79
Find the sum of the values then divide by the
number of values.
80+88+81+87+92+8
87
=35
7
Median
Test Scores
Arrange the values from least to greatest and find the middle value.
79,80, 8L,87,88,88,92
Mode
The mode is 88 since it is the number that occurs most ofben.
Range
Find the difference between the greatest and least values.
92
4;
E
-
79
:13
Example 2
Draw a box plot of the data in Example
1.
Draw a number line that includes the least and greatest numbers in the data.
Mark the minimum and maximum values, the median, and the fi.rst and third quartiles
above the number line. Draw the box plot and assign a title to the graph.
Test Scores
.9
79 80 81 82 83 84 85 86 87 88 89 90 91
92
.9
E
E
E
;
Exercise
Find the mean, median, mode, and range of the data set.
Then draw the box plot.
I
=
Scores
t57 161 165
160 161 160
159
157
F
o
1s6'rs7 158 159 160
Cource 5
16',1
162 163 164
. Chapter 9 Scatter Plots and Data Analysis
165
lt7
NAME
PERIOD
DATE
Lesson 5 Retearh
Measures of Variation
Example I
Find the mean absolute deviation of the nrrmber of downloads
shov,.n in the table. Describe what the mean absolute
deviation represents.
Find the mean. 9 + 6 + 11 i 9 + 5 + 8
b
Downloads
9611
958
- t
Find the absolute value of the differences between each data value and the mean.
le
lg
- 8l-- 1
- al: t
lrl - Bl:3
la - gl: o
- 8l= 2
15 - 8l: g
16
Find the average ofthe absolute values. 1 + 2 + 3 t 1 + 3 + 0
6
- r.,
The average distance each data value is flom the mean is about 1.7 downloads.
n
E
Example 2
The standard deviation of the data in Example 1 is aborut 2.2.
Descrihe the number of dov,'nloads that are within one standard
deviation of the mean.
E
Find the range of values that are within one standard deviation of the mean.
5
E
i
S - 2.2
8 + 2.2
{
: 5.8
: 10.2
Subtract the standard deviation from the mean.
Add the standard deviation to the mean.
E
E
Oownloads between 5.8 and 10.2 are
within one standard deviation of the mean.
-2
'a
b
!
A
5E.
Exetcises
1. Find the mean absolute deviation of the test scores shown
in the table. Describe what the mean absolute deviation means.
=
=
i
I
Test Scores
90 82 85 100
93 80 94 88
=
F
g
E
3
2. The standard deviation of the data in Exercise 1 is about 6.7. Describe
the data values that are within one standard deviation of the mean.
Course
I . Chapter 9 Scatter Plots and Data Analysis
r59
NAME
PERIOD
DATE
Lesson 6 Retearh
Analyze Data Distributrons
The distribution of data can be described by its center, spread (variation), and overall shape. lf data
on a line plot are symmetric, then the left side looks like the right side. Another way to describe the
shape of the distribution is to identify peaks, clusters, gaps, and outliers.
Example
BOOKS The graph shows the number of books
students read during the summer. Identiff any
s5rmmetry, clusters, gaps, peaks, or outliers in
thedistribution.
Books Read During the Summer
x
x x
III
x
xx
I
x
Thedistributionisnon-SJ[nmetricbecausetheleft
side does not look like the right side of the graph.
There is a cluster from 6 to 8 with a peak at 8.
There are two gaps. One gap is between 8 and 11 and
another gap between 14 and 19.
There is an outlier at 19.
Exercises
1. DANCE The number of years of experience in dance
for various students is shown in the graph.
a. Describe the shape of the distribution.
!
Years of Experiente
in Dance
Ero
o
E
g
.9
€
I
b. Identiff any clusters,
B
gaps, peaks, or outliers.
I
--
oJ
6o
I
E
zo
o-2 3-5 6-8 9-l I
Years oI Experience
-9
_9
.9
E
E,
A
!
J
!
ic
2.
CARS The number of cars sold each day is shown in
the graph.
Number oI Cars Sold
Each Day
a. Describe the shape of the distribution.
=
?
.qo
b. Identify any clusters, gaps, peaks, or outliers.
G
6789
Day
Cource
I . Chapter 9 Scatter Plots and Data Analysis
I4I
PERIOD
DATE
Lesson
I Reteach
Scatter Plots
A scatter plot shows the relationship between a data set with two variables graphed as ordered pairs.
The pattern of the data points determines the association between the two sets of data.
. Data points that go generally upward from left to right show a positive association.
. Data points that go generally downward from left to right show a negative association.
. Data points with no clear pattern show no association between the data sets.
Examples
Explain whether the scatter plot of the
data shows a positiae, negatiae, oT no
association. Interpret the scatter plot.
E8
=
$o
1. miles driven and gallons of gas used
o
24
c
As the number of miles driven increases, the amount of gas
used increases. Therefore, the scatter plot will show a
positive association. There appears to be a linear association.
Ez
0
50
100 150
200
Miles Driven
2. number of minutes a candle burns and a
candle's height
!
o
As the number of minutes increases, the height of the candle g4
o
will decrease. Therefore, the scatter plot will show a negative att
ba
association. There appears to be a linear association.
o
oi
E
0
Exercises
Explain whether the scatter plot of the data for each of the
following shows a positive, negatiae, ot no association.
Interpret the scatter plot.
r)
1.
.9
J
.g
J28
G
e7
!9
50
t9
.B
2
Ezo
o2
.2
E
9
soo
E
o
Ee
.E
E40
U
o
4S
E,
o
5t5
o
-20
EIO
Ez
o
I
!
05101520
3
o2468
=
fime (minutes)
positive; Sample answer:
As the age increases,
the height increases.
There appears to be a
linear association.
Counre
o r 234557
Day ol the tUeek
Ate (years)
o
'i
Shower
negative; Sample answer:
As the number of minutes
increases, the amount of
hot water decrcases.
There appears to be a
linear association.
I . Chapter 9 Scatter Plots and Data Analysis
no association;
Sample answer:The
day does not affect the
number of phone calls,
r29
NAME
PERIOD
DATE
Lesson 2 Retearh
Lrnes
of Best Fit
Examples
BOATS Boat sales at Dustin's Marina are given.
Week
1
2
t)
4
5
6
7
8
Boat Sales
2
3
5
8
6
10
8
18
1. Construct a scatter plot using the data. Then draw
and assess a line that seems to best represent
the data.
Graph each of the data points. Draw a line
that fits the data.
t8
14
3,
63e
6
4
2
o123456
Week
table shows the number of new
join
the Outdoor Club.
members to
CLUB The
e
Day
New Members
1
2
3
4
5
6
3
6
4
3
6
4
'a
.q
.9.
E
b.
=
F
o
I
n7
=
o_
=4
z5
1
Use the line of best frt to make a conjecture about the
number of new members to join the club on the eighth
o 121
day. Sample answer: 7 new members
2. PORTFOLIO The table shows the value of Heathey's
portfolio, in thousands ofdollars, at the end of
each year.
a90
€eo
o
Ezo
o
q.
Year
Value
50
1
2
3
4
5
6
?to
90
70
80
60
80
60
E40
950
a. Construct a scatter plot ofthe data. Then draw and
assess a line that seems to best represent the data.
b. Use the line of best frt to make
a conjecture about the
value of Heather's portfolio at the end of year 8.
Sample answer: $55,000
Course I . Chapter 9 Scatter Plots and Data Analysis
4567
DaY
I
g
0
9
36
E
bs
a. Construct a scatter plot ofthe data. Then draw and
assess a line that seems to best represent the data.
g
12
3ro
2. Use the line of best fit to make a conjecture about
boat sales in week 9.
Extend the line so that you can estimate the y-vaiue
for an r-value of 9. The y-value for the 9th week is
16 boats. We can predict that Dustin's Marina will
sell 16 boats in week 9.
Exercises
1. OUTDOOR
)'X
l6
€ro
tro
0 123 456789
Year
t5I
NAME
DATE
PEFIIOD
Lesson 5 Reteach
Two-Way lables
Example I
Marisa surveyed students at her school. She found that 30 out of 75 seventh
graders buy their lunch. There are 25 out of 76 eighth graders who do not buy
their lunch. Construct a two-way table summarizing the data.
Step 1 Create a table using the two-categories: buy lunch and grade level. Fill in the table
with the given values.
Step 2 IJse reasoning to complete the table. Remember, the totals are for each row and
column. The column labeled "Total" should have the same sum as the row labeled
"Total."
Buy Luneh
Do Not Buy Lunch
TotaI
30
45
75
51
25
76
81
70
151
Seventh Graders
Eishth Graders
Total
Erample 2
Find aud interpret the relative frequencies of seventh gladers in the survey fuom
Bvarnple I by row. Round to the nearest hundredth if necessary.
d
E
Seventh Graders
Eighth Graders
o
.9
.9
E
.9.
E
Total
# = 0.40
ur'
# x 0.67
45;#:0.60
rc,ff:
1.oo
zs,ff
,u,#=
1.00
30;
= 0.33
70
Total
151
Sample answer: Less than half of the seventh graders and more than half of the eighth
graders buy their lunch.
Exercise
f'ind and interpret the relative frequencies of seventh graders in the survey ftom
Example 1 by column. Bound to the nearest hundredth if necessary.
"Buy Lunch" cotumn:
=
F
Do Not Buy Lunch
81
3
o
Buy Lunch
column:
1.00; "Do Not Buy Lunch"
o.3Z;+ = 0.63,
3? =
€+ =
# * 0.64, # = 0.36,:+ :
1.00; Sample answer: Overatl, more than
half of the students surveyed buy their lunch.
Cource
! . Chapter 9 Scatter Plots and Data Analysis
r55
NAME
DATE
PERIOD
Lesson 4 Reteach
Descri pfive Statfstfcs
Example I
Find the mean, median, mode, and range of the data
shown in the table.
Mean
Test Scores
80 88 81
92 88 79
Find the sum of the values then divide by the
number of values.
87
80+88+81+87+92+88+79 :85
Median
Arrange the values from least to greatest and find the middle va1ue.
79,80,8L,87,88, Bg, 92
The mode is 88 since
Range
Find the difference between the greatest and least values.
92
a;
E
e
it is the number that
Mode
-
79
occurs most often.
:13
Example 2
Draw a box plot of the data in Example
1.
Draw a number line that includes the least and greatest numbers in the data.
Mark the minimum and maximum values, the median, and the first and third quartiles
above the number line. Draw the box plot and assign a title to the graph.
Test Scores
.!
79 80 81 82 83 84 85 86 87 88 89 90 91
'6
92
.9
E
d
E
.9
E
=3
g
I
E
Exercise
Find the mean, median, mode, and range of the data set.
Then draw the box plot.
mean 160, median 160, mode 160, range
-
F
o
-
-
Bowling Scores
-I
t57 161 165 159
160 161 160
157
Bowling Scores
156 157 158 159 160 161 162 163 164
Course
I . Chapter 9 Scatter Plots and Data Analysis
165
l17
PERIOD
DATE
Lesson 5 Retearh
Measures of Variation
Example I
Find the mean absolute deviation of the number of downloads
shown in the table. Describe what the mean absolute
deviation represents.
Findthemean.@:g
Downloads
9611
958
6
Find the absolute value of the differences between each data value and the mean.
lg-al:t
lg-sl:t
le-gl:z
l5-81=g
Find the average ofthe absolute values.
1
lrr-81=3
ls-sl:o
+2+3t 1+3+0
6
-
1.7
The average distance each data value is from the mean is about 1.7 downloads.
Example 2
The standard deviation of the data in Example I is about 2.2.
Describe the number of downloads that are within one standard
deviation of the mean.
g
E
f;
';
E
I
Find the range of values that are within one standard deviation of the mean.
i
Oownloads between 5.8 and 10.2 are
E
a - 2.2
8 + 2.2
: 5.8
: 10.2
Subtract the standard deviation from the mean.
Add the standard deviation to the mean.
within one standard deviation of the mean.
.9
:E
E
;
H
S
e.
I
E
Exercises
f. Find the mean absolute deviation of the test scores shown
in the table. Describe what the mean absolute deviation means.
S.25; Sample answer: The average distance each data
value is from the mean is 5.25 points.
Test Scores
90 82 85 100
93 80 94 88
6
E
.t
2. The standard deviation of the data in Exercise 1 is about 6.7. Describe
the data values that are within one standard deviation of the mean.
Test scores between 82.3 and 95.7 points are within one
standard deviation of the mean.
Course
I . Chapter 9 Scatter Plots and Data Analysis
t59
PERIOD
DATE
Lesson 6 Reteach
An
alyze Data
D
istributrbns
The distribution of data can be described by its center, spread (variation), and overall shape. lf data
on a line plot are symmetric, then the left side looks like the right side. Another way to describe the
shape of the distribution is to identify peaks, clusters, gaps, and outliers.
Example
BOOKS Ttre graph shows the number of books
students read during the summer. Identifu any
s5rmmetry, clusters, Saps, peaks, or outliers in
the distribution.
The distribution is non-symmetric because the left
side does not look like the right side of the graph.
Books Read During the Summer
x
xxx
xxx
xxx
5678
x
xx x
x
9 1011 121314151617181920
There is a cluster from 6 to 8 with a peak at 8.
There are two gaps. One gap is between 8 and 11 and
another gap between 14 and 19.
There is an outlier at 19.
.i
E
I
I
E
.9
.9
Exercises
1. DANCE The number of years of experience in dance
for various students is shown in the graph.
Years of Experiencc
in Dance
a. Describe the shape of the distribution.
The distribution is not symmetric.
€ro
-,o
oJ
o
G
b. Identifu any clusters, gaps, peaks, or outliers.
There is a cluster between 0 and 5 and no
gaps.There is a peak at the interval 3 to 5.
There are no outliers.
T
E
z,o
o-2 3-5 6-8 9-l
I
Years ol Experience
.E
,o
d
s
'
s
CARS The number of cars sold each day is shown in
the graph.
a. Describe the shape of the distribution.
The distribution is symmetric.
E
?20
G
c
Elo
I
zo
5
E
o
Number oI Cars Sold
Eath Day
b. Identifr any clusters, gaps, peaks, or outliers.
The data are centered around Z There are
no gaps. The peak of the data is at 7 and
there are no outliers.
Course
lt .
Chapter
9
Scatter Plots and Data Analysis
6789
Day
t4I