Five-number summary

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Topic: Five-number summary

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	Statistics: Power from Data! Five-number summary
		A five-number summary is especially useful in descriptive analyses or during the preliminary investigation of a large data set.
		To illustrate the five-number summary of Example 2 in the Range and quartiles section would be 1, 17, 26, 42, 57.
		In cases where we have more than one data set to analyse, a five-number summary with a corresponding box and whisker plot is constructed for each.
	www.statcan.ca /english/edu/power/ch12/five.htm (135 words)

	Five-Number Summary
		The five-number summary consists of the upper and lower extremes, the median, and the upper and lower quartile.
		The upper and lower extremes are the greatest and least numbers that occur in the set.
		The median is the middle term when the data is arranged from least to greatest.
	illuminations.nctm.org /Lessons/States/FiveNumSum.htm (206 words)

	IQR & 5-number summary
		The five-number summary consists of the minimum, maximum, median, and first and third quartiles of the sample distribution.
		The five-number summary is displayed visually using a boxplot (sometimes called a box-and-whiskers plot) (Chpt.
	www.esf.edu /for/bevilacqua/apm391/lecture3/tsld005.htm (33 words)

	Census of Fatal Occupational Injuries Summary, 2004
		The number of electrocutions also rose slightly, though the overall category of exposure to harmful substances and environments was lower due to declines in the numbers of fatalities resulting from contact with temperature extremes, exposure to caustic, noxious, or allergenic substances, and oxygen deficiency.
		The number of fatally injured Hispanic or Latino workers rose from 794 in 2003 to 883 in 2004, an increase of 11 percent.
		The number of workers who were fatally injured after being struck by objects rose 12 percent in 2004 (from 531 in 2003 to 596 in 2004), led by increases in the number of workers who were fatally injured after contact with falling, rolling, or sliding objects.
	www.bls.gov /news.release/cfoi.nr0.htm (2029 words)

	Summary Statistics: Location & Spread
		Sometimes the minimum and maximum are presented along with the median and the quartiles to provide a five number summary of the data.
		The mean and SD are a particularly appropriate summary for data whose histogram approximates a normal distribution (the bell-shaped curve).
		It is not counted as one of the summary statistics even though it fits the definition ("a function solely of the data") perfectly.
	www.tufts.edu /~gdallal/summary.htm (2909 words)

	SECTION 2C HIGHLIGHTS
		The five number summary is represented graphically using a box plot.
		The student should be able to find the five number summary for a data set.
		The student should be able to create a box-plot from a five number summary.
	www.sunybroome.edu /~mat_dept/current/1139bhl.htm (197 words)

	Measures of location
		If there are an odd number of data points, the median is the middle value, e.g., 5 for data set A. If there are an even number of data, the median is half way between the two middle values, e.g., (3+4)/2=3.5 for data set B and (155+155)/2=155 for the weights.
		Data set B has an even number of data; the lower and upper halves of the data set are {1,2,3} and {4,7,9} which provides that Q1 = 2 and Q3 = 7.
		A single number is often not adequate to convey where the data in a data set lie.
	www.cs.uni.edu /~campbell/stat/loc.html (1146 words)

	Module 1.3: Describing Data with Number Summaries
		The five number summary is complete when we add the minimum value of 16 and maximum of 29 days.
		Twenty five percent of the ordered observations in a set of data is contained within a quartile, so 25% of the observations are below the first quartile, 50% of the observations are below the 2nd quartile (Q2, also called the Median), and 75% of the observations are below the 3rd.
		Now subtract each number from the mean, square the result (to get rid of plusses and minuses), sum the resulting squared deviations, and divide by the number of numbers.
	ruby.fgcu.edu /courses/tharring/80890/m1_3.htm (5227 words)

	spread.html
		A useful set of summary numbers for a group of measurements is the median M, the lower and upper quartiles Q_L and Q_U, and the smallest and largest measurements, which we denote by LO and HI.
		The arithmetic average of the deviations is given by the sum of the deviations divided by the number of observations.
		In baseball, one measure of the quality of a hitter is the batting average which is defined to be the number of base hits divided by the number of official at-bats.
	www-math.bgsu.edu /~albert/m115/data/spread.html (2145 words)

	Summary of New 2002-06 CBA
		A player with more than 10 years in the majors, including at least five with his current club will be allowed, as part of a multiyear contract, waive his "10 and 5" right to block trades, so long as the waiver applies to no more than 13 teams.
		Seasons in which a player is optioned to the minors for fewer than 20 days won't count against the maximum number of seasons in which a player may be optioned; in return, players receive major league service time for the period of such assignments.
		Players with less than five years of major league service can be sent to a club's spring training facility for rehabilitation; however, each day starting with the 11th counts toward the maximum length for rehabilitation assignments (30 days for pitchers, 20 days for others)
	roadsidephotos.com /baseball/laborstatus.htm (1258 words)

	FRB: Beige Book - Summary
		Five of the districts indicated that conditions in telecommunications and other high-tech equipment manufacturing industries softened further during the survey period.
		Commercial construction was flat in most districts, although Cleveland and Richmond reported a modest number of projects underway or planned for the near future.
		Philadelphia indicated that banks were becoming more concerned about credit quality because a growing number of business borrowers had fallen short of revenue goals.
	www.federalreserve.gov /FOMC/BeigeBook/2001/20011128 (1780 words)

	TRAC Special Advisory on Terrorism
		The number of matters that the Justice Department classified as "terrorism" or "anti-terrorism" is sobering, considerably larger than suggested in department speeches, press releases and case-by-case news accounts.
		Despite this jump -- the number of convictions went from 96 to 341 -- the government's enforcement effort has not resulted in putting more terrorists behind bars for significant periods of time.
		Putting the anti-terrorism matters to one side, the government's case-by-case records show that in the post-9/11 period there were three and a half times more suspects convicted for what the government said were terrorist acts than in the pre-9/11 period.
	trac.syr.edu /media/news/newsadvisory031208.html (474 words)

	Encarta: The Discovery of Extrasolar Planets
		Also within five years the power of the two Keck telescopes on Mauna Kea will be joined together to form a device known as an optical interferometer that will provide sufficient precision to detect extrasolar planets the size of Earth.
		A seventh object, which orbits the star known by its catalog number HD114762, was first discovered in 1989 by astronomer David Latham of the Harvard-Smithsonian Center for Astrophysics in Cambridge, Massachusetts, and his collaborators.
		Within the next five years Doppler surveys of several hundred additional stars will begin at the 9-m (30-ft) Hobby-Eberly Telescope located at the McDonald Observatory, directed by Cochran.
	astron.berkeley.edu /~gmarcy/encarta.html (4764 words)

	Descriptive Statistics
		The five-number summary of the data consists of the minimum data point, the first quartile, the median, the third quartile, and the maximum data point.
		Thus these five numbers display the full range of variation (from minimum to maximum), the common range of variation (from first to third quartile), and a typical value (the median).
		Estimates of the range of variation seek to put a number to this common range of variation that doesn't depend on sample size.
	www.physics.csbsju.edu /stats/descriptive2.html (1632 words)

	Boxplots and five number summary
		Boxplots and the five number summary are useful for a variety of reasons in the statistics course.
		You can use the TRACE Key and the arrow key to actually identify the five number summary on the boxplot as is illustrated in the picture below
		They are especially useful for getting a quick picture of the distribution of the data, doing exploratory data analysis and comparing two datasets.
	wind.caspercollege.edu /~pwildman/statnew/new_page_14.htm (259 words)

	Five Pillars of Islam - Hutchinson encyclopedia article about Five Pillars of Islam
		Five Percent Nation of the Gods and the Earths
		Five Point Someone - What not to do at IIT
		This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.
	encyclopedia.farlex.com /Five%20Pillars%20of%20Islam (139 words)

	Apollo 13 Lunar Journal : Mission Summary
		To be sure, the Apollo 11 and 12 collections contained significant numbers of small rock fragments which differed markedly in composition from the bulk of the mare-derived materials; and there was every reason to believe that many of these "exotic" fragments represented ejecta from impacts in the distant highlands.
		The first came five hours after the accident and was designed to put them back on what was called a "free-return trajectory", a trajectory that would take them home even without the second burn.
		Apollo 13 was launched about five months after Conrad, Gordon and Bean returned from the Moon.
	www.hq.nasa.gov /office/pao/History/alsj/a13/a13.summary.html (3861 words)

	South Dakota v. Dole (1987) [86-260]
		The five percent loss of highway funds was not unduly coercive.
		In 1984, Congress enacted legislation ordering the Secretary of Transportation to withhold five percent of federal highway funds from states that did not adopt a 21-year-old minimum drinking age.
		The Court also held that the Twenty-first Amendment's limitations on spending power were not prohibitions on congressional attempts to achieve federal objectives indirectly.
	www.oyez.org /oyez/resource/case/363 (156 words)

	Mathwords: Five Number Summary
		Note: A boxplot is a visual display of the five-number summary.
		For a set of data, the minimum, first quartile, median, third quartile, and maximum.
	www.mathwords.com /f/five_number_summary.htm (34 words)

	The Year in Review
		Five Americans were killed in Jerusalem on 19 August when a suicide bomber riding on a bus detonated explosives attached to his body.
		In 2003, the highest number of attacks (70) and the highest casualty count (159 persons dead and 951 wounded) occurred in Asia.
		There were 82 anti-US attacks in 2003, which is up slightly from the 77 attacks the previous year, and represents a 62-percent decrease from the 219 attacks recorded in 2001.
	www.state.gov /s/ct/rls/pgtrpt/2003/31569.htm (825 words)

	Interrelations of summary statistics
		We have also seen the three quartiles used with the maximum and minimum in the five number summary.
		Histogram explorer provides another way to shape a histogram and look at the summary statistics.
		Applets: An interactive histogram illustrates how the summary statistics are related to a histogram.
	www.math.uni.edu /~campbell/stat/miscdesc.html (297 words)

	WHO Chernobyl: the true scale of the accident
		An estimated five million people currently live in areas of Belarus, Russia and Ukraine that are contaminated with radionuclides due to the accident; about 100 000 of them live in areas classified in the past by government authorities as areas of “strict control”.
		The report’s estimate for the eventual number of deaths is far lower than earlier, well-publicized speculations that radiation exposure would claim tens of thousands of lives.
		This number contains both the known radiation-induced cancer and leukaemia deaths and a statistical prediction, based on estimates of the radiation doses received by these populations.
	www.who.int /mediacentre/news/releases/2005/pr38/en (1750 words)

	Management of Chronic Asthma: Summary of Evidence Report/Technology Assessment, No. 44
		The full evidence report from which this summary was derived was prepared for AHRQ by the Blue Cross and Blue Shield Association's Technology Evaluation Center under contract number 290-97-0015.
		Because of the lack of additional trials and large numbers of withdrawals, the data are not sufficient to compare the relative effectiveness of ICS and theophylline.
		This study, with its large numbers and randomization and assessment of longitudinal changes, provides very strong evidence that there is no effect of ICS on BMD (in the doses given and time duration provided).
	www.ahrq.gov /clinic/epcsums/asthmasum.htm (5785 words)

	univar.hlp
		However, the output includes a five-number summary (minimum, 25th, 50th, 75th percentiles, and maximum) normally available only with the ^detail^ option of @summarize@.
		All plots occupy the same screen width and use the following scheme for representing the five-number summary: -----------------::::::::::::::::::::::::::------------------------- ^^ ^^ ^^ ^^ ^^ Min P25 P50 P75 Max ^byvar(^bylist^)^ displays a summary of the varlist variables for the subset of observations at each unique set of values of the bylist variables.
		^dec(^#^)^ controls the number of decimal places used in printing the summary values; the default value of # is 2.
	www.stata.com /stb/stb36/sg67/univar.hlp (416 words)

	Key Curriculum Press Fathom - Why Upgrade - Summary Tables
		The summary table now lets you add a set of basic statistics and/or the five-number statistics to a summary table with menu commands.
		Add numeric attributes to both dimensions of a summary table, and you get a flexible correlation matrix.
	www.keypress.com /fathom/pages/why_upgrade/summary_tables.php (40 words)

	Five Point Summary
		More detailed than reporting only median, but less detailed than showing a histogram or stem & leaf diagram, is the FIVE NUMBER SUMMARY:
		This plot of a five point summary is a BOX PLOT.
		The whiskers extend out to the least and largest numbers.
	www.math.unb.ca /~knight/BasicStat/fivept.htm (122 words)

	Test Number Three
		Conclusion: It is obvious from the five number summary that the average age at enlistment for each sample was about the same; however, the spread appears to have been larger in the Augusta sample.
		Five-number summaries and important statistics for each "Age" sample
		Because almost all Southern men fought for the Confederacy, this result should be intuitive: men of all ages fought for the South, while the North could afford to be more "picky."
	instruct1.cit.cornell.edu /courses/hist100.06/perkins/test3.htm (150 words)

	Tukey Five-Number Summaries
		A five number summary (minimum, lower-hinge, median, upper-hinge, maximum) for the numbers in
	www.math.montana.edu /Rweb/Rhelp/fivenum.html (13 words)

	Press Release ILO/04/47: New ILO book explores "Decent Working Time Deficit" in the industrialized countries
		By contrast, in most EU countries (prior to the 2004 expansion) the number of people working 50 hours or more per work remains well under 10 per cent, with figures ranging from 1.4 per cent in the Netherlands to 6.2 in Greece and Ireland.
		The publication concludes that finding the balance between business requirements and workers' needs will require working time policies along five dimensions: promoting health and safety; helping workers to better meet their family responsibilities; encouraging gender equality; advancing productivity; and facilitating worker choice and influence over their working hours.
		The book includes studies from five specialists on the issue of working time in Australia, the European Union, Japan, New Zealand and the United States.
	www.ilo.org /public/english/bureau/inf/pr/2004/47.htm (677 words)

	BCG News & Media - Media Releases
		Sixty percent of the executives in the industrial goods sector-which represents four of the world's top five spenders on R&D, with just those four spending over $26 billion on R&D in 2004 alone-were dissatisfied with their returns on innovation investments.
		A belief that incremental innovations aren't adequate in the current environment is potentially intensifying executives' concerns and doubts about their companies' innovation capabilities, according to the report.
		In addition, 64 percent of energy executives were dissatisfied with their innovation ROI, as were 56 percent in health care and 54 percent in financial services.
	www.bcg.com /news_media/news_media_releases.jsp?id=1318 (967 words)

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In the News (Sat 2 Jun 12)