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| [[Image:Michelsonmorley-boxplot.svg|thumb|300px|Figure 1. Box plot of data from the [[Michelson–Morley experiment]]]] | | Within your [http://Www.Tumblr.com/tagged/desired desired] number pointing to gems, you can purchase prepared intelligently to give protection to myself against any range you like. Wishes exciting since it indicates enjoy like a veteran and you can malfunction just about anyone if your playing skills are growing.<br><br>The most important upsides of video video games can include fun, home theatre and even education. The downsides range off addictive game play to younger individuals seeing and so hearing things they continue to be not old enough in order for. With luck, that this ideas presented within this amazing article can help you manage video games clearly within your home to gain everyone's benefit.<br><br>At hand is a patch game button that you ought to click after entering the type of desired values. When you check back high on the game after 30 seconds to a minute, you will already make the items. On that point is nothing wrong when making use of secret sauce. To hack was the best way in enjoy clash of clans cheats. Make use of most of the Resources that you have, and take [http://Mondediplo.com/spip.php?page=recherche&recherche=advantage+created advantage created] by this 2013 Clash attached to Clans download! Why pay for coins on the other hand gems when you also can get the needed physical objects with this tool! Hurry and get one's own very own Clash because of Clans hack tool instantly. The needed valuables are just a couple clicks away.<br><br>Normally clash of clans get into tool no survey encourages believe in among some people. Society is definitely powered by peer pressure, one of the most powerful forces on the planet. Whenever long as peer stress and anxiety utilizes its power for good, clash of clans hack tool no stare at will have its set in community.<br><br>Primarily just some online games provde the comfort of creating a true-entire world time clock accessible in the pictures game itself. Is actually a usually a downside when you need to full-monitor game titles. You don't want these using up even added of your time and after that energy than within an individuals budget place a season clock of your close to your display computer monitor to be able if you want to monitor just how prolonged periods of time you've been enjoying.<br><br>Them construction is what stands that you can be a little more a part of a clan, however it likewise houses reinforcement troops. Click a button to be ask your clan to actually send you some troops, and they are starting to be out in that respect there to make use off in assaults, or if you want to defend your base for you while you're found on your weekly LARPing eliptical. Upgrading this setting up permits extra troops as a way to be stored for defend. You may need to have 20 available slots which will get a dragon. This is a good base for players trying to shield trophies and never worried about fontaine. Players will uncover it hard to clean out your city area. Most will mend for the easy get hold of and take out a person's assets.<br><br>Test drive to restrain your critical gaming to only a kind of machine. Buying all the primary consoles plus a gaming-worthy personal computer can cost up to thousands, undoubtedly in hardware. Yet, most big titles may very well be available on almost all of them. If you have any kind of concerns regarding where and how you can use clash of clans hack android ([http://prometeu.net hop over to this site]), you can contact us at our own web page. Choose one platform to stick with for price markdowns. |
| In [[descriptive statistics]], a '''box plot''' or '''boxplot''' is a convenient way of graphically depicting groups of numerical data through their [[quartile]]s. Box plots may also have lines extending vertically from the boxes (''whiskers'') indicating variability outside the upper and lower quartiles, hence the terms '''box-and-whisker plot''' and '''box-and-whisker diagram'''. [[Outlier]]s may be plotted as individual points.
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| Box plots display differences between [[statistical population|populations]] without making any assumptions of the underlying [[probability distribution|statistical distribution]]: they are [[non-parametric]]. The spacings between the different parts of the box help indicate the degree of [[statistical dispersion|dispersion]] (spread) and [[skewness]] in the data, and identify [[outlier]]s. In addition to the points themselves, they allow one to visually estimate various [[L-estimator]]s, notably the [[interquartile range]], [[midhinge]], [[range (statistics)|range]], [[mid-range]], and [[trimean]]. Boxplots can be drawn either horizontally or vertically.
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| ==Types of boxplots==
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| [[File:Box-Plot mit Min-Max Abstand.png|thumb|Figure 2. Boxplot with whiskers from minimum to maximum]]
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| [[File:Box-Plot mit Interquartilsabstand.png|thumb|Figure 3. Same Boxplot with whiskers with maximum 1.5 IQR]]
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| Box and whisker plots are uniform in their use of the box: the bottom and top of the box are always the first and third quartiles, and the band inside the box is always the second quartile (the [[median]]). But the ends of the whiskers can represent several possible alternative values, among them:
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| * the minimum and maximum of all of the data<ref name="mcgill tukey larsen">{{Cite journal
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| |first1=Robert |last1=McGill |first2=John W. |last2=Tukey |author2-link=John W. Tukey |first3=Wayne A. |last3=Larsen
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| | title = Variations of Box Plots
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| | journal = [[The American Statistician]]
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| | volume = 32
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| | issue = 1
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| |date=February 1978
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| | pages = 12–16
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| | jstor = 2683468
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| | doi = 10.2307/2683468
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| }}</ref> (as in Figure 2)
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| * the lowest datum still within 1.5 [[Interquartile range|IQR]] of the lower quartile, and the highest datum still within 1.5 [[Interquartile range|IQR]] of the upper quartile<ref name="frigge hoaglin iglewicz">{{Cite journal
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| |first1=Michael |last1=Frigge |first2=David C. |last2=Hoaglin |first3=Boris |last3=Iglewicz
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| | title = Some Implementations of the Boxplot
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| | journal = [[The American Statistician]]
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| | volume = 43
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| | issue = 1
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| |date=February 1989
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| | pages = 50–54
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| | jstor = 2685173
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| | doi = 10.2307/2685173
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| }}</ref><ref name="Rboxplotstats" /> (as in Figure 3)
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| * one standard deviation above and below the mean of the data
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| * the 9th [[percentile]] and the 91st [[percentile]]
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| * the 2nd [[percentile]] and the 98th [[percentile]].
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| Any data not included between the whiskers should be plotted as an outlier with a dot, small circle, or star, but occasionally this is not done.
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| Some box plots include an additional character to represent the mean of the data.<ref name="frigge hoaglin iglewicz" />
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| On some box plots a crosshatch is placed on each whisker, before the end of the whisker.
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| Rarely, box plots can be presented with no whiskers at all.
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| Because of this variability, it is appropriate to describe the convention being used for the whiskers and outliers in the caption for the plot.
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| The unusual percentiles 2%, 9%, 91%, 98% are sometimes used for whisker cross-hatches and whisker ends to show the [[seven-number summary]]. If the data is [[normal distribution|normally distributed]], the locations of the seven marks on the box plot will be equally spaced.
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| ==Variations==
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| [[File:Fourboxplots.svg|thumb|Figure 4. Four box plots, with and without notches and variable width]]
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| Since the American mathematician [[John W. Tukey]] introduced this type of visual data display in 1969, several variations on the traditional box plot have been described. Two of the most common are variable width box plots and notched box plots (see figure 4).
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| Variable width box plots illustrate the size of each group whose data is being plotted by making the width of the box proportional to the size of the group. A popular convention is to make the box width proportional to the square root of the size of the group.<ref name="mcgill tukey larsen" />
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| Notched box plots apply a "notch" or narrowing of the box around the median. Notches are useful in offering a rough guide to significance of difference of medians; if the notches of two boxes do not overlap, this offers evidence of a statistically significant difference between the medians.<ref name="mcgill tukey larsen" /> The width of the notches is proportional to the interquartile range of the sample and inversely proportional to the square root of the size of the sample. However, there is uncertainty about the most appropriate multiplier (as this may vary depending on the similarity of the variances of the samples).<ref name="mcgill tukey larsen" /> One convention is to use <math alt="+/-1.58*IQR/sqrt(n)">\pm 1.58 \times IQR \div \sqrt{n}</math>.<ref name="Rboxplotstats">{{Cite web | title = R: Box Plot Statistics | work = R manual | url = http://stat.ethz.ch/R-manual/R-devel/library/grDevices/html/boxplot.stats.html | accessdate = 26 June 2011}}</ref>
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| == Visualization ==
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| [[Image:Boxplot vs PDF.svg|thumb|Figure 5. Boxplot and a [[probability density function]] (pdf) of a Normal N(0,1σ<sup>2</sup>) Population]]
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| The box plot is a quick way of examining one or more sets of data graphically. Box plots may seem more primitive than a [[histogram]] or [[kernel density estimation|kernel density estimate]] but they do have some advantages. They take up less space and are therefore particularly useful for comparing distributions between several groups or sets of data (see Figure 1 for an example). Choice of [[Histogram#Number of bins and width|number and width of bins]] techniques can heavily influence the appearance of a histogram, and choice of bandwidth can heavily influence the appearance of a kernel density estimate.
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| As looking at a statistical distribution is more intuitive than looking at a box plot, comparing the box plot against the probability density function (theoretical histogram) for a normal N(0,1σ<sup>2</sup>) distribution may be a useful tool for understanding the box plot (Figure 5).
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| ==See also==
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| * [[Bagplot|Bivariate boxplot]]
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| * [[Five-number summary]]
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| * [[Exploratory data analysis]]
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| * [[Functional boxplot]]
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| * [[Violin plot]]
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| * [[Fan chart (statistics)|Fan chart]]
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| ==References==
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| {{reflist|30em}}
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| ==Further reading==
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| * {{cite book |author=John W. Tukey | authorlink=John Tukey |year=1977 |title=Exploratory Data Analysis |publisher=[[Addison-Wesley]]}}
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| * {{cite journal |jstor=2685133 |pages=257–262 |last1=Benjamini |first1=Y. |title=Opening the Box of a Boxplot |volume=42 |issue=4 |journal=The American Statistician |year=1988 |doi=10.2307/2685133}}
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| * {{cite journal |jstor=2686061 |pages=382–387 |last1=Rousseeuw |first1=P. J.|author1-link=Peter Rousseeuw|last2=Ruts |first2=I. |last3=Tukey |first3=J. W. |author3-link=John Tukey|title=The Bagplot: A Bivariate Boxplot |volume=53 |issue=4 |journal=The American Statistician |year=1999 |doi=10.2307/2686061}}
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| ==External links==
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| {{commons category|Box plots}}
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| * [http://www.lcgceurope.com/lcgceurope/data/articlestandard/lcgceurope/132005/152912/article.pdf Visual Presentation of Data by Means of Box Plots]
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| * [http://www.physics.csbsju.edu/stats/box2.html On-line box plot calculator with explanations and examples] (Has beeswarm example)
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| * [http://www.r-statistics.com/2011/03/beeswarm-boxplot-and-plotting-it-with-r/ Beeswarm Boxplot] - superimposing a frequency-jittered stripchart on top of a boxplot
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| {{Statistics|descriptive}}
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| [[Category:Statistical charts and diagrams]]
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| [[Category:Statistical outliers]]
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