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The following box plot shows the U.S. population for 1990, the latest available year. (Source: Bureau of the Census, 1990 Census)

A box plot with values from 0 to 105, with Q1 at 17, M at 33, and Q3 at 50.
  • Are there fewer or more children (age 17 and under) than senior citizens (age 65 and over)? How do you know?
  • 12.6% are age 65 and over. Approximately what percent of the population are of working age adults (above age 17 to age 65)?
  • more children
  • 62.4%
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Javier and Ercilia are supervisors at a shopping mall. Each was given the task of estimating the mean distance that shoppers live from the mall. They each randomly surveyed 100 shoppers. The samples yielded the following information:

Javier Ercilla
x 6.0 miles 6.0 miles
s 4.0 miles 7.0 miles
  • How can you determine which survey was correct?
  • Explain what the difference in the results of the surveys implies about the data.
  • If the two histograms depict the distribution of values for each supervisor, which one depicts Ercilia's sample? How do you know?
    Two histograms.  The first plot shows a fairly symmetrical distribution with a mode of 6.  The second plot shows a uniform distribution.
  • If the two box plots depict the distribution of values for each supervisor, which one depicts Ercilia’s sample? How do you know?
    Two box plots.  The first has values from 0 to 21 with Q1 at 1, M at 6, and Q3 at 14.  The second plot has values from 0 to 12 with Q1 at 4, M at 6, and Q3 at 9.
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Student grades on a chemistry exam were:

  • 77, 78, 76, 81, 86, 51, 79, 82, 84, 99

  • Construct a stem-and-leaf plot of the data.
  • Are there any potential outliers? If so, which scores are they? Why do you consider them outliers?
  • 51,99
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Try these multiple choice questions (exercises 24 - 30).

The next three questions refer to the following information. We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.

Number of years Frequency
Total = 20
7 1
14 3
15 1
18 1
19 4
20 3
22 1
23 1
26 1
40 2
42 2

What is the IQR?

  • 8
  • 11
  • 15
  • 35

A

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What is the mode?

  • 19
  • 19.5
  • 14 and 20
  • 22.65

A

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Is this a sample or the entire population?

  • sample
  • entire population
  • neither

B

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The next two questions refer to the following table. X = the number of days per week that 100 clients use a particular exercise facility.

x Frequency
0 3
1 12
2 33
3 28
4 11
5 9
6 4

The 80th percentile is:

  • 5
  • 80
  • 3
  • 4

D

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The number that is 1.5 standard deviations BELOW the mean is approximately:

  • 0.7
  • 4.8
  • -2.8
  • Cannot be determined

A

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The next two questions refer to the following histogram. Suppose one hundred eleven people who shopped in a special T-shirt store were asked the number of T-shirts they own costing more than $19 each.

A histogram showing the results of a survey.  Of 111 respondents, 5 own 1 t-shirt costing more than $19, 17 own 2, 23 own 3, 39 own 4, 25 own 5, 2 own 6, and no respondents own 7.

The percent of people that own at most three (3) T-shirts costing more than $19 each is approximately:

  • 21
  • 59
  • 41
  • Cannot be determined

C

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If the data were collected by asking the first 111 people who entered the store, then the type of sampling is:

  • cluster
  • simple random
  • stratified
  • convenience

D

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Below are the 2010 obesity rates by U.S. states and Washington, DC. ( Source: http://www.cdc.gov/obesity/data/adult.html) )

State Percent (%) State Percent (%)
Alabama 32.2 Montana 23.0
Alaska 24.5 Nebraska 26.9
Arizona 24.3 Nevada 22.4
Arkansas 30.1 New Hampshire 25.0
California 24.0 New Jersey 23.8
Colorado 21.0 New Mexico 25.1
Connecticut 22.5 New York 23.9
Delaware 28.0 North Carolina 27.8
Washington, DC 22.2 North Dakota 27.2
Florida 26.6 Ohio 29.2
Georgia 29.6 Oklahoma 30.4
Hawaii 22.7 Oregon 26.8
Idaho 26.5 Pennsylvania 28.6
Illinois 28.2 Rhode Island 25.5
Indiana 29.6 South Carolina 31.5
Iowa 28.4 South Dakota 27.3
Kansas 29.4 Tennessee 30.8
Kentucky 31.3 Texas 31.0
Louisiana 31.0 Utah 22.5
Maine 26.8 Vermont 23.2
Maryland 27.1 Virginia 26.0
Massachusetts 23.0 Washington 25.5
Michigan 30.9 West Virginia 32.5
Minnesota 24.8 Wisconsin 26.3
Mississippi 34.0 Wyoming 25.1
Missouri 30.5
  • Construct a bar graph of obesity rates of your state and the four states closest to your state. Hint: Label the x-axis with the states.
  • Use a random number generator to randomly pick 8 states. Construct a bar graph of the obesity rates of those 8 states.
  • Construct a bar graph for all the states beginning with the letter "A."
  • Construct a bar graph for all the states beginning with the letter "M."

Example solution for b using the random number generator for the Ti-84 Plus to generate a simple random sample of 8 states. Instructions are below.

  • Number the entries in the table 1 - 51 (Includes Washington, DC; Numbered vertically)
  • Press MATH
  • Arrow over to PRB
  • Press 5:randInt(
  • Enter 51,1,8)
Eight numbers are generated (use the right arrow key to scroll through the numbers). The numbers correspond to the numbered states (for this example: {47 21 9 23 51 13 25 4}. If any numbers are repeated, generate a different number by using 5:randInt(51,1)). Here, the states (and Washington DC) are {Arkansas, Washington DC, Idaho, Maryland, Michigan, Mississippi, Virginia, Wyoming}. Corresponding percents are {28.7 21.8 24.5 26 28.9 32.8 25 24.6}. A bar graph showing 8 states on the x-axis and corresponding obesity rates on the y-axis.

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A music school has budgeted to purchase 3 musical instruments. They plan to purchase a piano costing $3000, a guitar costing $550, and a drum set costing $600. The mean cost for a piano is $4,000 with a standard deviation of $2,500. The mean cost for a guitar is $500 with a standard deviation of $200. The mean cost for drums is $700 with a standard deviation of $100. Which cost is the lowest, when compared to other instruments of the same type? Which cost is the highest when compared to other instruments of the same type. Justify your answer numerically.

For pianos, the cost of the piano is 0.4 standard deviations BELOW the mean. For guitars, the cost of the guitar is 0.25 standard deviations ABOVE the mean. For drums, the cost of the drum set is 1.0 standard deviations BELOW the mean. Of the three, the drums cost the lowest in comparison to the cost of other instruments of the same type. The guitar cost the most in comparison to the cost of other instruments of the same type.

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Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in the previous month. The results are summarized in the table below. (Note that this is the data presented for publisher B in homework exercise 13).

Publisher b
# of books Freq. Rel. Freq.
0 18
1 24
2 24
3 22
4 15
5 10
7 5
9 1
  1. Are there any outliers in the data? Use an appropriate numerical test involving the IQR to identify outliers, if any, and clearly state your conclusion.
  2. If a data value is identified as an outlier, what should be done about it?
  3. Are any data values further than 2 standard deviations away from the mean? In some situations, statisticians may use this criteria to identify data values that are unusual, compared to the other data values. (Note that this criteria is most appropriate to use for data that is mound-shaped and symmetric, rather than for skewed data.)
  4. Do parts (a) and (c) of this problem give the same answer?
  5. Examine the shape of the data. Which part, (a) or (c), of this question gives a more appropriate result for this data?
  6. Based on the shape of the data which is the most appropriate measure of center for this data: mean, median or mode?

  • IQR = 4 – 1 = 3 ; Q1 – 1.5*IQR = 1 – 1.5(3) = -3.5 ; Q3 + 1.5*IQR = 4 + 1.5(3) = 8.5 ;The data value of 9 is larger than 8.5. The purchase of 9 books in one month is an outlier.
  • The outlier should be investigated to see if there is an error or some other problem in the data; then a decision whether to include or exclude it should be made based on the particular situation. If it was a correct value then the data value should remain in the data set. If there is a problem with this data value, then it should be corrected or removed from the data. For example: If the data was recorded incorrectly (perhaps a 9 was miscoded and the correct value was 6) then the data should be corrected. If it was an error but the correct value is not known it should be removed from the data set.
  • xbar – 2s = 2.45 – 2*1.88 = -1.31 ; xbar + 2s = 2.45 + 2*1.88 = 6.21 ; Using this method, the five data values of 7 books purchased and the one data value of 9 books purchased would be considered unusual.
  • No: part (a) identifies only the value of 9 to be an outlier but part (c) identifies both 7 and 9.
  • The data is skewed (to the right). It would be more appropriate to use the method involving the IQR in part (a), identifying only the one value of 9 books purchased as an outlier. Note that part (c) remarks that identifying unusual data values by using the criteria of being further than 2 standard deviations away from the mean is most appropriate when the data are mound-shaped and symmetric.
  • The data are skewed to the right. For skewed data it is more appropriate to use the median as a measure of center.

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**Exercises 32 and 33 contributed by Roberta Bloom

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Damian Reply
absolutely yes
Daniel
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Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.
Nerisha Reply

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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