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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%

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.

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

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

What is the mode?

  • 19
  • 19.5
  • 14 and 20
  • 22.65

A

Is this a sample or the entire population?

  • sample
  • entire population
  • neither

B

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

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

  • 0.7
  • 4.8
  • -2.8
  • Cannot be determined

A

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

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

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.

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.

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.

**Exercises 32 and 33 contributed by Roberta Bloom

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Collaborative statistics for mt230. OpenStax CNX. Aug 18, 2011 Download for free at http://legacy.cnx.org/content/col11345/1.2
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