Chapter
2:( activity) pls upload your answer on FB..deadline is on july 22, 2012
2.1
The top ten movies and their profits (in millions of
dollars) from the weekend of May
23–25, 1997, are presented here:
The Lost World: Jurassic
Park $90.2 Father’s Day $4.7
Addicted to Love 11.4 Liar Liar 3.0
The Fifth Element 8.0 Volcano 2.3
Austin Powers 5.6 NightFalls on Manhattan 2.1
Breakdown 5.4 Anaconda 1.73
a.
Draw a stem and leaf plot for
the data.
Are the data skewed?
NO,
because in my observation in the stem and leaf plot I’ve made, there is an
outlier data which is the 90.2.
a.
Calculate the mean profit for
these ten movies for the May 23–25 weekend. Calculate the median profit.
Calculating the mean profit…..
c.
Which of the two measures in
part b best describes the center of the data? Explain.
In part b, the measure of median profit
describes the center of the data. One of the reason is it determines the center
value of the profit. Median is always understood by the statisticians as the
center value.
2.2
Does birth order have any effect on a person’s
personality?
Based
in my observation or in relating in the real life, the birth order can affect a
person’s personality. The oldest child is more responsible than the young ones
but dependent to their social, financial status in their family. But most
situation, oldest are smarter and responsible. The reason is that their parents have more time with
them and as the number of child increases, the older child is task to take good
care of them.
A report on a study by an MIT researcher
indicates that later born children are more likely to challenge the
establishment, more open to new ideas, and more accepting of change. In fact,
the number of later born children is increasing. During the Depression years of
the 1930s, families averaged 2.5 children (59% later born), whereas the parents
of baby boomers averaged 3 to 4 children (68% later born).
What does the author mean by an average of 2.5 children?
The author mean by an average of 2.5
children as 2-3 children. 2.5 is the value when adding 2 & 3 and the sum is
divided by the 2.
2.3
The Internet has
captured the attention and interest of many Americans. In fact, the number of
hours spent “online” has been steadily increasing over the last few years. It
is projected that the average time spent online in the year 1999 will be 14
hours per person per year. Suppose that the standard deviation of the
distribution of x, the number of hours
per person per year spent online, is 20 hours.
a.
Visualize the distribution of
hours per year spent online.
The
distribution of hours per year spent online is increasing to many Americans.
Why do you suppose
the yearly average for the entire U.S. population is so low?
Because the
standard deviation is greater than the average number of hours per person per year
spent online.
b.
Do you think the distribution
is relatively mound-shaped, skewed right, or skewed left? Explain.
The distribution is skewed right because
the averaged distribution of hours spent online is increasing.
c.
Within what limits would you expect
at least 3/4 of the measurements to lie?
14 – 20 hours
2.4
Refer to Exercise 2.3. You can use the Empirical Rule to
see why the distribution of hours per person per year could not be
mound-shaped.
a.
Find the value of x that is exactly one standard deviation below the mean.
The value of x must be lesser than the
mean.
b.
If the distribution is
in fact mound-shaped, approximately what percentage of the measurements should
be less than the value of x found in part a?
25% of the measurements should be less than
the value of x found in part a.
c.
Since the variable
being measured is “hours per year,” is it possible to find any measurements
that are more than one standard deviation below the mean? Explain.
Yes, as long as there are lots of data
collected.
d.
Use your answers to
parts b and c to explain why the data distribution cannot be mound-shaped.
The reason is the mean and median are not
really equal.
2.5
In a review of several textbooks for use in high school
biology instruction, the number of chapters and the number of pages in each of
seven textbooks were recorded as shown here:
Textbook Chapters Pages
 |
Biology: The Study of Life 39 885
Biology: The Dynamics of Life 36 779
Biology Today 54 887
Biological Science: A Molecular
Approach 26 599
Biological Science: An Ecological
Approach 24 689
Health Biology 50 849
Modern Biology 53 831
a.
Calculate z-scores for
the number of chapters in Biology Today and Biological
Science: An Ecological Approach. Does either of the books have an unusually large or
small number of chapters?
Therefore, there is no unusually large or
small number of chapters.
b.
Construct a box plot
for the numbers of chapters in the seven books.
List of data
(chapters):
24, 26, 36, 39, 50, 53, 54
Q1 position :
.25(n + 1) = .25(7 + 1) = 2nd
position
Q1 = 26
Q3 position :
.75(n + 1) = .75(7 + 1) = 6th
position
Q3 = 53
Median position:
.5(n+1) = .5(7 + 1) = 4th
position
m = 39
IQR = Q3 - Q1 = 53 – 26
IQR
= 27
Box
plot:
Does
the box plot confirm your answer in part a?
YES…
a.
Use a box plot to
describe the distribution of the numbers of pages in the seven books.
List of data (pages): 599, 689, 779, 831, 849, 885, 887
Q1 position :
.25(n + 1) = .25(7 + 1) = 2nd
position
Q1 = 689
Q3 position :
.75(n + 1) = .75(7 + 1) = 6th
position
Q3 = 885
Median position:
.5(n+1) = .5(7 + 1) = 4th
position
m = 831
IQR = Q3 - Q1 = 885 - 689
IQR
= 196
Box plot:
2.6
The state of California
not only has some of the most polluted metropolitan areas in the country but
also has some of the strictest pollution regulations in the country. As a
result of an aggressive campaign by the South Coast Air Quality Management
District (AQMD),the amount of pollution in southern California’s atmosphere is beginning to
decrease. One of its regulations requires employers of 100 or more workers to
prepare a ride-sharing plan that offers incentives for workers to share a ride,
telecommute, ride a bike, or take public transportation to work. The goal is to
have 1.5 workers per car during morning rush hours. What does the AQMD mean by
this goal statement?
The goal statement means that 1-2 workers must ride in a
car or more. Which means workers must use a car with higher capacity to load
more than two workers.
2.7
American Demographics is a magazine that investigates various aspects of life
in the United States
using all sorts of descriptive statistics.
These facts were noted in a recent issue:
§
26% of all U.S.
adults between the ages of 18 and 24 own five or more pairs of wearable
sneakers.
§
61% of U.S.
households have two or more television sets.
Identify any percentiles that can be determined from
this information.
§
74% of U.S. population aging less or greater than 18-24 year old
has less than five pairs of sneakers.
§
39% of U.S. households own only one TV set.
2.8
The top 20
movies and their gross revenues (in millions of dollars) from Labor Day weekend
(August 31-September 3, 2001) are shown below:
|
Movie
|
Weekend
Gross
|
Movie
|
Weekend
Gross
|
|
Jeepers Creepers
|
$15.8
|
Planet of the Apes
|
$3.8
|
|
Rush Hour 2
|
11.7
|
Jurassic Park III
|
2.3
|
|
American Pie 2
|
11.0
|
John Carpenter’s Ghosts of Mars
|
2.1
|
|
The Others
|
10.2
|
The Curse of the Jade Scorpion
|
2.0
|
|
Rat Race
|
9.2
|
The Deep End
|
1.8
|
|
The Princess Diaries
|
7.6
|
Legally Blonde
|
1.7
|
|
O
|
6.9
|
America’s Sweethearts
|
1.3
|
|
Jay and Silent Bob Strike Back
|
6.5
|
American Outlaws
|
1.3
|
|
Summer Catch
|
4.9
|
Bubble Boy
|
1.3
|
|
Captain Corelli’s Mandolin
|
3.9
|
Pearl Harbor
|
1.2
|
a.
Can you
tell by looking at the data whether it is roughly symmetric? NO
Or is it
skewed? SKEWED
b.
Calculate
the mean and the median. Use these measures
to decide whether or not the data are symmetric or skewed.
m = 3.85
Mean > Median … Therefore, the data is
skewed right.
a.
Draw a box
plot to describe the data.
List of data: 1.2, 1.3, 1.3, 1.3, 1.7, 1.8, 2.0, 2.1,
2.3, 3.8, 3.9, 4.9, 6.5, 6.9, 7.6, 9.2, 10.2, 11.0, 11.7, 15.8
Q1
position :
.25(n
+ 1) = .25(20 + 1) = 5.25nd position
Q1
= 1.8 + .25(1.8 – 1.7)
Q1
= 1.83
Q3
position :
.75(n
+ 1) = .75(20 + 1) = 15.75th position
Q3 = 9.2 + .75(9.2 –
7.8)
Q3
= 10.25
Median position:
.5(n+1)
= .5(20 + 1) = 10.5th position
m = 
m = 3.85
IQR = Q3 - Q1 = 10.25 – 1.83
IQR = 8.42
Box Plot:
Explain why
the box plot confirms your conclusions in part b.
The data are arranged slantly.
2.9
The gross
revenue (in millions of dollars) for the top 20 movies over the 2001 Labor Day
weekend (Exercise 2.41 and data set EX0241) are reproduced below7:
15.8 11.7 11.0 10.2 9.2 7.6 6.9 6.5 4.9 3.9
3.8
2.3 2.1 2.0 1.8 1.7 1.3 1.3 1.3 1.2
a.
Calculate
the mean and standard deviation for these 20 observations.
a. b.
Calculate
the z-score for the largest and
smallest observations (
and
). Should
either movie, Jeepers Creepers or Pearl Harbor,
be considered unusual?
and). Should
either movie, Jeepers Creepers or Pearl Harbor,
be considered unusual?
a. c.
Construct a
box plot for the data, or refer to the box plot drawn in Exercise 2.41. Does the box plot confirm your results in
part b? [HINT: Since the
z-score and the box plots are two
unrelated methods for detecting outliers, and use different types of
statistics, they do not necessarily have to (but usually do) produce the same
results.]
List of data: 1.2, 1.3, 1.3, 1.3, 1.7, 1.8, 2.0, 2.1,
2.3, 3.8, 3.9, 4.9, 6.5, 6.9, 7.6, 9.2, 10.2, 11.0, 11.7, 15.8
Q1
position :
.25(n
+ 1) = .25(20 + 1) = 5.25nd position
Q1
= 1.8 + .25(1.8 – 1.7)
Q1
= 1.83
Q3
position :
.75(n
+ 1) = .75(20 + 1) = 15.75th position
Q3 = 9.2 + .75(9.2 –
7.8)
Q3
= 10.25
Median position:
.5(n+1)
= .5(20 + 1) = 10.5th position
m = 
m = 3.85
IQR = Q3 - Q1 = 10.25 – 1.83
IQR = 8.42
Box plot:
YES, the box plot confirm my answer in
part b.
2.10
LCD
TVs
The cost of televisions exhibits huge variation – from $100-200 for a
standard TV to $8000-10,000 for a large plasma screen TV. Consumer
Reports gives the prices for the top ten LCD standard definition TVs in the
14- to 20-inch category:
|
Brand
|
Price
|
|
Sharp
LC-20E1U
Sony
KLV-15SR1
Panasonic
TC-20LA1
Panasonic
TC-17LA1
Gateway
GTW-L18M103
Panasonic
TC-14LA1
Gateway
GTW-L17M103
Toshiba
14VL43U
Toshiba
20VL43U
Sharp
LC-15E1U
|
$1200
800
1050
750
700
500
600
670
1200
650
|
a.
What other variables would be important to
you? The other variable important to me is the quality of the
product.
2.11
Brett
Favre
The number of passes completed by Bret Favre, quarterback for the Green
Bay Packers, was recorded at each of the 16 regular season and 2 postseason
games in the fall of 2003 (ESPN.com):
|
25
|
15
|
23
|
21
|
19
|
25
|
|
23
|
18
|
14
|
13
|
10
|
23
|
|
22
|
23
|
22
|
12
|
26
|
15
|
a.
Draw a stem and leaf plot to
describe the data.
where 1 | 5 = 15
RE ORDER:
where 1 | 5 =15
b.
Calculate the mean and standard
deviation for Brett Favre’s per-game pass completions.
c.
What proportion of the
measurements lie within two standard deviations of the mean?
¼ of the measurements lie within two standard deviations of the
mean.
2.12
Comparing
NFL Quarterbacks
How does Brett Favre, quarterback for the Green Bay Packers, compare to
Donovan McNabb, quarterback for the Philadelphia Eagles? The table below shows the number of completed
passes for each athlete during the 2003 NFL football season (ESPN.com):
|
Brett Favre
|
Donovan McNabb
|
||||||
|
|
a.
Calculative five-number summaries
for the number of passes completed by both Brett Favre and Donovan McNabb.
b. Construct
box plots for the two sets of data.
|
Brett Favre
|
||
|
25
|
23
|
22
|
|
15
|
18
|
23
|
|
23
|
14
|
22
|
|
21
|
13
|
12
|
|
19
|
10
|
26
|
|
25
|
23
|
15
|
List
of data: 10 12 13 14 15 15 18 19 21 22 22 23 23 23 23 25
25 26
Position
of median:
0.5 (n+1) = 9.5th position
Median = (21 +22) / 2 = 21.5
– average of the 9th& 10th data
Position
of Q1:
0.25
(n+1) = 0.25 (18+1)= 4.75th position
Q1
is ¾ between 4th& 5th
Q1
= 14 + 0.75(15- 14)
Q1 = 14. 75
Position
of Q3:
0.75
(n+1) = 0.75 (18+1) = 14.25th position
Q3
is ¼ between 14th& 15th
Q3
= 23 + 0.25 (23- 23)
Q3
= 23
IQR
= Q3 – Q1 = 23 – 14. 75
IQR = 8.25
Box
plot:
Are there any
outliers? NO
-
What do the box plots tell you about the
shapes of the two distributions? It is skewed left
because the median line is at the right of the center and has a long left
whisker.
|
Donovan
McNabb
|
||
|
19
|
17
|
18
|
|
18
|
21
|
15
|
|
18
|
15
|
27
|
|
16
|
24
|
23
|
|
11
|
16
|
21
|
|
9
|
18
|
10
|
List
of Data: 9 10 11 15 15 16 16 17 18 18 18 18 19 21 21 23 24 27
Position of median:
0.5
(n+1) = 9.5th position
Median = (18+18) / 2 = 18
– average of the 9th& 10th data
Position
of Q1:
0.25
(n+1) = 0.25 (18+1) = 4.75th position
Q1
is ¾ between 4th& 5th
Q1
= 15 + 0.75(15- 15)
Q1 = 15
Position
of Q3 :
0.75 (n+1)
= 0.75 (18+1) = 14.25th
position
Q3
is ¼ between 14th& 15th
Q3
= 21 + 0.25 (21- 21)
Q3 = 21
IQR
= Q3 – Q1 = 21 – 15
IQR = 6
Box plot:
Are there any
outliers? NO
-
What do the box plots tell you about the
shapes of the two distributions? It is mound-shaped.
c.
Write a short paragraph comparing
the number of pass completions for the two quarterbacks.
The number of pass completions for two
quarterbacks of Brett Favre, quarterback for the Green Bay Packers has lesser
completion compare to Donovan McNabb quarterback for the Philadelphia Eagles.
Brett Favre has skewed distribution while Donovan McNabb has mount shaped
distribution.
2.13
Internet
Hotspots
The most visited site on the Internet is Yahoo!, which boasted 111,271
thousand unique visitors in December 2003 (Exercise 1.21 and data set
EX0121). The number of unique visitors
at the top 25 sites are shown in the table:
|
Site
|
Unique
Visitors
(Millions)
|
|
Site
|
Unique
Visitors
(Millions)
|
|
Yahoo!
Sites
Time
Warner Network
MSN-Microsoft
Sites
EBay
Google
Sites
Terra
Lycos
Amazon
Sites
About/Primedia
Excite
Network
CNET
Networks
Walt
Disney Internet
Viacom
Online
American
Greetings
|
111.3
110.5
110.0
69.2
61.5
52.1
45.7
42.6
25.1
25.1
25.1
24.7
24.4
|
|
Weather
Channel
Real.com
Network
Verizon
Communications
Wal-Mart
Shopping.com
Sites
Symantec
AT&T
Properties
InfoSpace
Network
Monster
Property
EA
Online
SBC
Communications
Sony
Online
|
23.8
22.3
22.1
21.4
21.3
19.9
17.5
17.3
17.3
16.8
16.5
16.5
|
Source: cyberatlas.internet.com
a.
Can you tell by looking at the
data whether it is roughly symmetric? YES
Or is it skewed? SKEWED
b.
Calculate the mean and the
median. Use these measures to decide
whether or not the data are symmetric or skewed.
Calculating the mean…
= 960 / 25
c.
Draw a box plot to describe the data.
Position
of Q1 :
0.25 (n+1) =
0.25 (25+1) = 6.5th
position
Q1
is ½ between 6th& 7th, 52.1 & 45.7
Q1
= 17.5 + 0.5(17.5-17.3)
Q1 =
17.6
Position
of Q3 :
0.75
(n+1) = 0.75 (25+1) = 19.5th position
Q3
is ½ between 19th& 20th, 19.9 & 17.5
Q3
= 52.1 + 0.5 (52.1- 45.7)
Q3
= 55.3
IQR
= Q3 – Q1 = 55.3 – 17.6
IQR = 37.7
Box
plot:
Explain why the box plot confirms
your conclusions in part b.
The distribution of data are slanted to left.
2.14
Snapshots Here are a few facts reported as snapshots
in USA Today.
·
Fifty-two percent of Americans
believe that the ideal family size is 2 or fewer children.
·
Seventy percent of Americans
reheat leftovers in their microwave at least two times a week.
·
Fifty percent of Americans
typically wait 15 minutes or less to have a prescription filled.
Identify
the variable x being measured, and
any percentiles you can determine from this information.
- The
variable x being measured is the American Population.
-
Thirty percent (30%) of Americans either reheat leftovers once a week or not at
all.
-
Forty-eight (48%) of Americans believe that the ideal family has more than 2
children.
-
Fifty percent (50%) of Americans wait for more than 15 minutes to have a
prescription filled.
Answer all the activity given!
---
:D Hello to you!
Hmm.. Those were just made due to deadline!
hehehe...
if you have some corrections, i'm glad if you have, then comment immediately! Don't think twice. I stand to be corrected.
I'm not perfect...
Once, you want the document file of it, email me or message me.
miss_yannie@yahoo.com
...
Those aren't correct answers.
Remember that!
...
Sweet,
LRJG
Walang komento:
Mag-post ng isang Komento