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1.3 Frequency, frequency tables, and levels of measurement  (Page 4/14)

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From [link] , find the number of towns that have rainfall between 2.95 and 9.01 inches.

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6 + 7 + 15 = 28 towns

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Collaborative exercise

In your class, have someone conduct a survey of the number of siblings (brothers and sisters) each student has. Create a frequency table. Add to it a relative frequency column and a cumulative relative frequency column. Answer the following questions:

     
  1. What percentage of the students in your class have no siblings?
  2. What percentage of the students have from one to three siblings?
  3. What percentage of the students have fewer than three siblings?

Nineteen people were asked how many miles, to the nearest mile, they commute to work each day. The data are as follows:

  • 2
  • 5
  • 7
  • 3
  • 2
  • 10
  • 18
  • 15
  • 20
  • 7
  • 10
  • 18
  • 5
  • 12
  • 13
  • 12
  • 4
  • 5
  • 10
. [link] was produced:

Frequency of commuting distances
DATA FREQUENCY RELATIVE
FREQUENCY		 CUMULATIVE
RELATIVE
FREQUENCY
3 3 3 19 0.1579
4 1 1 19 0.2105
5 3 3 19 0.1579
7 2 2 19 0.2632
10 3 4 19 0.4737
12 2 2 19 0.7895
13 1 1 19 0.8421
15 1 1 19 0.8948
18 1 1 19 0.9474
20 1 1 19 1.0000
  1. Is the table correct? If it is not correct, what is wrong?
  2. True or False: Three percent of the people surveyed commute three miles. If the statement is not correct, what should it be? If the table is incorrect, make the corrections.
  3. What fraction of the people surveyed commute five or seven miles?
  4. What fraction of the people surveyed commute 12 miles or more? Less than 12 miles? Between five and 13 miles (not including five and 13 miles)?
  1. No. The frequency column sums to 18, not 19. Not all cumulative relative frequencies are correct.
  2. False. The frequency for three miles should be one; for two miles (left out), two. The cumulative relative frequency column should read: 0.1052, 0.1579, 0.2105, 0.3684, 0.4737, 0.6316, 0.7368, 0.7895, 0.8421, 0.9474, 1.0000.
  3. 5 19
  4. 7 19 , 12 19 , 7 19
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[link] represents the amount, in inches, of annual rainfall in a sample of towns. What fraction of towns surveyed get between 11.03 and 13.05 inches of rainfall each year?

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9 50

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[link] contains the total number of deaths worldwide as a result of earthquakes for the period from 2000 to 2012.

Year Total Number of Deaths
2000 231
2001 21,357
2002 11,685
2003 33,819
2004 228,802
2005 88,003
2006 6,605
2007 712
2008 88,011
2009 1,790
2010 320,120
2011 21,953
2012 768
Total 823,356

Answer the following questions.

  1. What is the frequency of deaths measured from 2006 through 2009?
  2. What percentage of deaths occurred after 2009?
  3. What is the relative frequency of deaths that occurred in 2003 or earlier?
  4. What is the percentage of deaths that occurred in 2004?
  5. What kind of data are the numbers of deaths?
  6. The Richter scale is used to quantify the energy produced by an earthquake. Examples of Richter scale numbers are 2.3, 4.0, 6.1, and 7.0. What kind of data are these numbers?
  1. 97,118 (11.8%)
  2. 41.6%
  3. 67,092/823,356 or 0.081 or 8.1 %
  4. 27.8%
  5. Quantitative discrete
  6. Quantitative continuous
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[link] contains the total number of fatal motor vehicle traffic crashes in the United States for the period from 1994 to 2011.

Year Total Number of Crashes Year Total Number of Crashes
1994 36,254 2004 38,444
1995 37,241 2005 39,252
1996 37,494 2006 38,648
1997 37,324 2007 37,435
1998 37,107 2008 34,172
1999 37,140 2009 30,862
2000 37,526 2010 30,296
2001 37,862 2011 29,757
2002 38,491 Total 653,782
2003 38,477

Answer the following questions.

  1. What is the frequency of deaths measured from 2000 through 2004?
  2. What percentage of deaths occurred after 2006?
  3. What is the relative frequency of deaths that occurred in 2000 or before?
  4. What is the percentage of deaths that occurred in 2011?
  5. What is the cumulative relative frequency for 2006? Explain what this number tells you about the data.

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  1. 190,800 (29.2%)
  2. 24.9%
  3. 260,086/653,782 or 39.8%
  4. 4.6%
  5. 75.1% of all fatal traffic crashes for the period from 1994 to 2011 happened from 1994 to 2006.
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References

“State&County QuickFacts,” U.S. Census Bureau. http://quickfacts.census.gov/qfd/download_data.html (accessed May 1, 2013).

“State&County QuickFacts: Quick, easy access to facts about people, business, and geography,” U.S. Census Bureau. http://quickfacts.census.gov/qfd/index.html (accessed May 1, 2013).

“Table 5: Direct hits by mainland United States Hurricanes (1851-2004),” National Hurricane Center, http://www.nhc.noaa.gov/gifs/table5.gif (accessed May 1, 2013).

“Levels of Measurement,” http://infinity.cos.edu/faculty/woodbury/stats/tutorial/Data_Levels.htm (accessed May 1, 2013).

Courtney Taylor, “Levels of Measurement,” about.com, http://statistics.about.com/od/HelpandTutorials/a/Levels-Of-Measurement.htm (accessed May 1, 2013).

David Lane. “Levels of Measurement,” Connexions, http://cnx.org/content/m10809/latest/ (accessed May 1, 2013).

Chapter review

Some calculations generate numbers that are artificially precise. It is not necessary to report a value to eight decimal places when the measures that generated that value were only accurate to the nearest tenth. Round off your final answer to one more decimal place than was present in the original data. This means that if you have data measured to the nearest tenth of a unit, report the final statistic to the nearest hundredth.

In addition to rounding your answers, you can measure your data using the following four levels of measurement.

  • Nominal scale level: data that cannot be ordered nor can it be used in calculations
  • Ordinal scale level: data that can be ordered; the differences cannot be measured
  • Interval scale level: data with a definite ordering but no starting point; the differences can be measured, but there is no such thing as a ratio.
  • Ratio scale level: data with a starting point that can be ordered; the differences have meaning and ratios can be calculated.

When organizing data, it is important to know how many times a value appears. How many statistics students study five hours or more for an exam? What percent of families on our block own two pets? Frequency, relative frequency, and cumulative relative frequency are measures that answer questions like these.

What type of measure scale is being used? Nominal, ordinal, interval or ratio.

  1. High school soccer players classified by their athletic ability: Superior, Average, Above average
  2. Baking temperatures for various main dishes: 350, 400, 325, 250, 300
  3. The colors of crayons in a 24-crayon box
  4. Social security numbers
  5. Incomes measured in dollars
  6. A satisfaction survey of a social website by number: 1 = very satisfied, 2 = somewhat satisfied, 3 = not satisfied
  7. Political outlook: extreme left, left-of-center, right-of-center, extreme right
  8. Time of day on an analog watch
  9. The distance in miles to the closest grocery store
  10. The dates 1066, 1492, 1644, 1947, and 1944
  11. The heights of 21–65 year-old women
  12. Common letter grades: A, B, C, D, and F
  1. ordinal
  2. interval
  3. nominal
  4. nominal
  5. ratio
  6. ordinal
  7. nominal
  8. interval
  9. ratio
  10. interval
  11. ratio
  12. ordinal
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Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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