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Pie chartFrom Wikipedia, the free encyclopedia

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Pie chart of populations ofEnglishnative speakers

A pie chart (or a circle graph) is acircularchart divided into sectors, illustrating proportion. In a pie chart, the arc lengthofeach sector (and consequently itscentral angleand area), isproportionalto the quantity it represents. When angles are measuredwith 1turnas unit then a number of percent is identified with the same number of centiturns. Together, the sectors create a fulldisk. It is named for its resemblance to apie which has been sliced. The earliest known pie chart is generally credited toWilliamPlayfair'sStatistical Breviary of 1801.[1][2]

The pie chart is perhaps the most ubiquitous statistical chart in the business world and the mass media.[3]However, it has beencriticized,[4] and some recommend avoiding it,[5][6][7][8]pointing out in particular that it is difficult to compare different sections of agiven pie chart, or to compare data across different pie charts. Pie charts can be an effective way of displaying information insome cases, in particular if the intent is to compare the size of a slice with the whole pie, rather than comparing the slices amongthem.[1]Pie charts work particularly well when the slices represent 25 to 50% of the data,[9]but in general, other plots such as the

bar chart or thedot plot, or non-graphical methods such astables, may be more adapted for representing certain information.Italso shows the frequency within certain groups of information.

Contents

[hide]

1 Example

2 Use, effectiveness and visual perception

3 Variants and similar charts

3.1 Exploded pie chart

3.2 Polar area diagram

3.3 Spie chart

3.4 Multi-level Pie, Radial tree, or Ring

chart

3.5 3-D pie chart

3.6 Doughnut chart

4 History

5 Notes

6 See also

7 References
http://en.wikipedia.org/wiki/English_languagehttp://en.wikipedia.org/wiki/English_languagehttp://en.wikipedia.org/wiki/Circlehttp://en.wikipedia.org/wiki/Circlehttp://en.wikipedia.org/wiki/Charthttp://en.wikipedia.org/wiki/Charthttp://en.wikipedia.org/wiki/Circular_sectorhttp://en.wikipedia.org/wiki/Arc_lengthhttp://en.wikipedia.org/wiki/Arc_lengthhttp://en.wikipedia.org/wiki/Central_anglehttp://en.wikipedia.org/wiki/Central_anglehttp://en.wikipedia.org/wiki/Central_anglehttp://en.wikipedia.org/wiki/Areahttp://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Turn_(geometry)http://en.wikipedia.org/wiki/Turn_(geometry)http://en.wikipedia.org/wiki/Turn_(geometry)http://en.wikipedia.org/wiki/Piehttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/Bar_charthttp://en.wikipedia.org/wiki/Dot_plot_(statistics)http://en.wikipedia.org/wiki/Dot_plot_(statistics)http://en.wikipedia.org/wiki/Table_(information)http://en.wikipedia.org/wiki/Table_(information)http://en.wikipedia.org/wiki/Table_(information)http://en.wikipedia.org/wiki/Pie_charthttp://en.wikipedia.org/wiki/File:English_dialects1997.svghttp://en.wikipedia.org/wiki/File:English_dialects1997.svghttp://en.wikipedia.org/wiki/English_languagehttp://en.wikipedia.org/wiki/Circlehttp://en.wikipedia.org/wiki/Charthttp://en.wikipedia.org/wiki/Circular_sectorhttp://en.wikipedia.org/wiki/Arc_lengthhttp://en.wikipedia.org/wiki/Central_anglehttp://en.wikipedia.org/wiki/Areahttp://en.wikipedia.org/wiki/Proportionality_(mathematics)http://en.wikipedia.org/wiki/Turn_(geometry)http://en.wikipedia.org/wiki/Piehttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/Bar_charthttp://en.wikipedia.org/wiki/Dot_plot_(statistics)http://en.wikipedia.org/wiki/Table_(information)http://en.wikipedia.org/wiki/Pie_chart


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[edit] Example

A pie chart for the example data.

The following example chart is based on preliminary results of the election for the European Parliament in 2004. The table liststhe number of seats allocated to each party group, along with the derived percentage of the total that they each make up. Thevalues in the last column, the derived central angle of each sector, is found by multiplying the percentage by 360.

Group Seats Percent (%) Central angle ()

EUL 39 5.3 19.2

PES 200 27.3 98.4

EFA 42 5.7 20.7

EDD 15 2.0 7.4ELDR 67 9.2 33.0

EPP 276 37.7 135.7

UEN 27 3.7 13.3

Other 66 9.0 32.5

Total 732 99.9* 360.2*

*Because of rounding, these totals do not add up to 100 and 360.

The size of each central angle is proportional to the size of the corresponding quantity, here the number of seats. Since the sum ofthe central angles has to be 360, the central angle for a quantity that is a fraction Q of the total is 360Q degrees. In the example,the central angle for the largest group (European People's Party (EPP)) is 135.7 because 0.377 times 360, rounded to onedecimal place(s), equals 135.7.

[edit] Use, effectiveness and visual perception

Three sets ofdata plotted using pie charts and bar charts.

Pie charts are common in business and journalism[citation needed]. Howeverstatisticiansgenerally regard pie charts as a poor methodof displaying information, and they are uncommon in scientific literature. One reason is that it is more difficult for comparisonsto be made between the size of items in a chart when area is used instead of length and when different items are shown asdifferent shapes. Stevens' power lawstates that visual area is perceived with a power of 0.7, compared to a power of 1.0 forlength. This suggests that length is a better scale to use, since perceived differences would be linearly related to actualdifferences.
http://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=1http://en.wikipedia.org/wiki/European_Parliament_election,_2004http://en.wikipedia.org/wiki/European_Parliament_election,_2004http://en.wikipedia.org/wiki/European_United_Left%E2%80%93Nordic_Green_Lefthttp://en.wikipedia.org/wiki/Party_of_European_Socialistshttp://en.wikipedia.org/wiki/European_Free_Alliancehttp://en.wikipedia.org/wiki/Europe_of_Democracies_and_Diversitieshttp://en.wikipedia.org/wiki/European_Liberal_Democrat_and_Reform_Partyhttp://en.wikipedia.org/wiki/European_People's_Partyhttp://en.wikipedia.org/wiki/Union_for_Europe_of_the_Nationshttp://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=2http://en.wikipedia.org/wiki/Data_plothttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Statisticianshttp://en.wikipedia.org/wiki/Statisticianshttp://en.wikipedia.org/wiki/Statisticianshttp://en.wikipedia.org/wiki/Stevens'_power_lawhttp://en.wikipedia.org/wiki/Stevens'_power_lawhttp://en.wikipedia.org/wiki/File:Piecharts.svghttp://en.wikipedia.org/wiki/File:Piecharts.svghttp://en.wikipedia.org/wiki/File:Pie_chart_EP_election_2004.svghttp://en.wikipedia.org/wiki/File:Pie_chart_EP_election_2004.svghttp://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=1http://en.wikipedia.org/wiki/European_Parliament_election,_2004http://en.wikipedia.org/wiki/European_United_Left%E2%80%93Nordic_Green_Lefthttp://en.wikipedia.org/wiki/Party_of_European_Socialistshttp://en.wikipedia.org/wiki/European_Free_Alliancehttp://en.wikipedia.org/wiki/Europe_of_Democracies_and_Diversitieshttp://en.wikipedia.org/wiki/European_Liberal_Democrat_and_Reform_Partyhttp://en.wikipedia.org/wiki/European_People's_Partyhttp://en.wikipedia.org/wiki/Union_for_Europe_of_the_Nationshttp://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=2http://en.wikipedia.org/wiki/Data_plothttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Statisticianshttp://en.wikipedia.org/wiki/Stevens'_power_law


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Further, in research performed at AT&T Bell Laboratories, it was shown that comparison by angle was less accurate thancomparison by length. This can be illustrated with the diagram to the right, showing three pie charts, and, below each of them, thecorresponding bar chart representing the same data. Most subjects have difficulty ordering the slices in the pie chart by size;when the bar chart is used the comparison is much easier.[10] Similarly, comparisons between data sets are easier using the barchart. However, if the goal is to compare a given category (a slice of the pie) with the total (the whole pie) in a single chart andthe multiple is close to 25 or 50 percent, then a pie chart can often be more effective than a bar graph.[11]

However, the research of Spence and Lewandowsky did not find pie charts to be inferior.[12][13]Participants were able to estimate

values with pie charts just as well as with other presentation forms.

[edit] Variants and similar charts

[edit] Exploded pie chart

An exploded pie chart for the example data, with the largest party group exploded.

A chart with one or more sectors separated from the rest of the disk is known as an exploded pie chart. This effect is used toeither highlight a sector, or to highlight smaller segments of the chart with small proportions.

[edit] Polar area diagram

"Diagram of the causes of mortality in the army in the East" by Florence Nightingale.

The polar area diagram is similar to a usual pie chart, except sectors are equal angles and differ rather in how far each sectorextends from the center of the circle. The polar area diagram is used to plot cyclic phenomena (e.g., count of deaths by month).For example, if the count of deaths in each month for a year are to be plotted then there will be 12 sectors (one per month) allwith the same angle of 30 degrees each. The radius of each sector would be proportional to the square root of the death count forthe month, so the area of a sector represents the number of deaths in a month. If the death count in each month is subdivided bycause of death, it is possible to make multiple comparisons on one diagram, as is clearly seen in the form of polar area diagramfamously developed byFlorence Nightingale.

The first known use of polar area diagrams was byAndr-Michel Guerry, which he called courbes circulaires, in an 1829 papershowing seasonal and daily variation in wind direction over the year and births and deaths by hour of the day.[14]Lon Lalannelater used a polar diagram to show the frequency of wind directions around compass points in 1843. The wind rose is still used

bymeteorologists. Nightingale published her rose diagram in 1858. The name "coxcomb" is sometimes used erroneously: thiswas the name Nightingale used to refer to a book containing the diagrams rather than the diagrams themselves.[15] It has beensuggested[by whom?] that most of Nightingale's early reputation was built on her ability to give clear and concise presentations ofdata.

[edit] Spie chart
http://en.wikipedia.org/wiki/AT&T_Bell_Laboratorieshttp://en.wikipedia.org/wiki/AT&T_Bell_Laboratorieshttp://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=4http://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=5http://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Andr%C3%A9-Michel_Guerryhttp://en.wikipedia.org/wiki/Andr%C3%A9-Michel_Guerryhttp://en.wikipedia.org/wiki/Andr%C3%A9-Michel_Guerryhttp://en.wikipedia.org/w/index.php?title=L%C3%A9on_Lalanne&action=edit&redlink=1http://en.wikipedia.org/wiki/Meteorologisthttp://en.wikipedia.org/wiki/Meteorologisthttp://en.wikipedia.org/wiki/Meteorologisthttp://en.wikipedia.org/wiki/Wikipedia:Avoid_weasel_wordshttp://en.wikipedia.org/wiki/Wikipedia:Avoid_weasel_wordshttp://en.wikipedia.org/wiki/Wikipedia:Avoid_weasel_wordshttp://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=6http://en.wikipedia.org/wiki/File:Nightingale-mortality.jpghttp://en.wikipedia.org/wiki/File:Nightingale-mortality.jpghttp://en.wikipedia.org/wiki/File:Pie_chart_EP_election_2004_exploded.pnghttp://en.wikipedia.org/wiki/File:Pie_chart_EP_election_2004_exploded.pnghttp://en.wikipedia.org/wiki/AT&T_Bell_Laboratorieshttp://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=4http://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=5http://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Andr%C3%A9-Michel_Guerryhttp://en.wikipedia.org/w/index.php?title=L%C3%A9on_Lalanne&action=edit&redlink=1http://en.wikipedia.org/wiki/Meteorologisthttp://en.wikipedia.org/wiki/Wikipedia:Avoid_weasel_wordshttp://en.wikipedia.org/w/index.php?title=Pie_chart&action=edit&section=6


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A useful variant of the polar area chart is the spie chart designed by Feitelson .[16]This superimposes a normal pie chart with amodified polar area chart to permit the comparison of a set of data at two different states. For the first state, for example time 1, anormal pie chart is drawn. For the second state, the angles of the slices are the same as in the original pie chart, and the radii varyaccording to the change in the value of each variable. In addition to comparing a partition at two times (e.g. this year's budgetdistribution with last year's budget distribution), this is useful for visualizing hazards for population groups (e.g. the distributionof age and gener groups among road casualties compared with these groups's sizes in the general population). The R GraphGallery provides an example.[17]

[edit] Multi-level Pie, Radial tree, or Ring chart

Multi-level pie or Ring chart of Disk usage in Linux file system

Multi-level pie chart, also known as a radial tree chart is used to visualize hierarchical data, depicted by concentric circles.[18]Thecircle in the centre represents the root node, with the hierarchy moving outward from the center. A segment of the inner circle

bears a hierarchical relationship to those segments of the outer circle which lie within the angular sweep of the parent segment. [19]

[edit] 3-D pie chart

Aperspective (3D) pie chart is used to give the chart a3Dlook. Often used for aesthetic reasons, the third dimension does notimprove the reading of the data; on the contrary, these plots are difficult to interpret because of the distorted effect ofperspectiveassociated with the third dimension. The use of superfluous dimensions not used to display the data of interest is discouraged forcharts in general, not only for pie charts.[7][20]

[edit] Doughnut chart

A doughnut chart (also spelled donut) is functionally identical to a pie chart, with the exception of a blank center and the abilityto support multiple statistics as one.

[edit] History

The earliest known pie chart is generally credited toWilliam Playfair's Statistical Breviary of 1801, in which two such graphs areused.[1][2] This invention was not widely used at first;[1] the French engineerCharles Joseph Minard was one of the first to use it in1858, in particular in maps where he needs to add information in a third dimension.[21]
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One of William Playfair's pie charts in his Statistical Breviary, depicting the proportions of the Turkish Empirelocated inAsia,Europeand Africabefore 1789.

Minard's map using pie charts to represent the cattle sent from all around Francefor consumption inParis(1858).

Line chartFrom Wikipedia, the free encyclopedia


This simple graph shows data over intervals with connected points

A line chart orline graph is a type ofgraph, which displays information as a series of data points connected bystraightlinesegments.[1]It is a basic type ofchartcommon in many fields. It is an extension of a scatter graph, and is

created by connecting a series of points that represent individual measurements with line segments. A line chart isoften used to visualize a trend in data over intervals of time atime series thus the line is often drawnchronologically.[2]

[edit] Example

In the experimental sciences, data collected from experiments are often visualized by a graph that includes anoverlaid mathematical function depicting thebest-fittrend of the scattered data. This layer is referred to as a best-fitlayer and the graph containing this layer is often referred to as a line graph.

For example, if one were to collect data on the speed of a body at certain points in time, one could visualize the databy adata table such as the following:
http://en.wikipedia.org/wiki/Ottoman_Empirehttp://en.wikipedia.org/wiki/Ottoman_Empirehttp://en.wikipedia.org/wiki/Asiahttp://en.wikipedia.org/wiki/Asiahttp://en.wikipedia.org/wiki/Europehttp://en.wikipedia.org/wiki/Europehttp://en.wikipedia.org/wiki/Europehttp://en.wikipedia.org/wiki/Africahttp://en.wikipedia.org/wiki/Africahttp://en.wikipedia.org/wiki/Francehttp://en.wikipedia.org/wiki/Francehttp://en.wikipedia.org/wiki/Parishttp://en.wikipedia.org/wiki/Parishttp://en.wikipedia.org/wiki/Parishttp://en.wikipedia.org/wiki/Graph_of_a_functionhttp://en.wikipedia.org/wiki/Graph_of_a_functionhttp://en.wiktionary.org/wiki/linehttp://en.wiktionary.org/wiki/linehttp://en.wiktionary.org/wiki/linehttp://en.wikipedia.org/wiki/Charthttp://en.wikipedia.org/wiki/Charthttp://en.wikipedia.org/wiki/Charthttp://en.wikipedia.org/wiki/Scatter_graphhttp://en.wikipedia.org/wiki/Scatter_graphhttp://en.wikipedia.org/wiki/Time_serieshttp://en.wikipedia.org/wiki/Time_serieshttp://en.wikipedia.org/wiki/Time_serieshttp://en.wikipedia.org/w/index.php?title=Line_chart&action=edit&section=1http://en.wikipedia.org/wiki/Best-fithttp://en.wikipedia.org/wiki/Best-fithttp://en.wikipedia.org/wiki/Data_tablehttp://en.wikipedia.org/wiki/Data_tablehttp://en.wikipedia.org/wiki/File:Graph_(PSF).pnghttp://en.wikipedia.org/wiki/File:Graph_(PSF).pnghttp://en.wikipedia.org/wiki/File:Minard-carte-viande-1858.pnghttp://en.wikipedia.org/wiki/Ottoman_Empirehttp://en.wikipedia.org/wiki/Asiahttp://en.wikipedia.org/wiki/Europehttp://en.wikipedia.org/wiki/Africahttp://en.wikipedia.org/wiki/Francehttp://en.wikipedia.org/wiki/Parishttp://en.wikipedia.org/wiki/Graph_of_a_functionhttp://en.wiktionary.org/wiki/linehttp://en.wikipedia.org/wiki/Charthttp://en.wikipedia.org/wiki/Scatter_graphhttp://en.wikipedia.org/wiki/Time_serieshttp://en.wikipedia.org/w/index.php?title=Line_chart&action=edit&section=1http://en.wikipedia.org/wiki/Best-fithttp://en.wikipedia.org/wiki/Data_table


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Graph of Speed Vs Time

Elapsed Time (s) "Speed" (ms1)

0 0

1 32 7

3 12

4 20

5 30

6 45

The table "visualization" is a great way of displaying exact values, but a very bad way of understanding theunderlying patterns that those values represent. Because of these qualities, the table display is often erroneouslyconflated with the data itself; whereas it is just another visualization of the data.

Understanding the process described by the data in the table is aided by producing a graph or line chart ofSpeedversus Time. In this context,Versus (or the abbreviations vs andVS), separates the parameters appearing in an X-Y(two-dimensional) graph. The first argument indicates the dependent variable, usually appearing on the Y-axis,

while the second argument indicates the independent variable, usually appearing on the X-axis. So, the graph ofSpeed versus Time would plot time along the x-axis and speed up the y-axis. Mathematically, if we denote time by

the variable t, and speed by v, then the function plotted in the graph would be denoted v(t) indicating that v (thedependent variable) is a function oft.

It is simple to construct a "best-fit" layer consisting of a set of line segments connecting adjacent data points;however, such a "best-fit" is usually not an ideal representation of the trend of the underlying scatter data for thefollowing reasons:

1. It is highly improbable that the discontinuities in the slope of the best-fit would correspond exactly with thepositions of the measurement values.

2. It is highly unlikely that the experimental error in the data is negligible, yet the curve falls exactly througheach of the data points.

A true best-fit layer should depict a continuous mathematical function whose parameters are determined by using asuitable error-minimization scheme, which appropriately weights the error in the data values.

In either case, the best-fit layer can reveal trends in the data. Further, measurements such as the gradientor the areaunder the curve can be made visually, leading to more conclusions or results from the data.

Time seriesFrom Wikipedia, the free encyclopedia

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Time series: random data plus trend, with best-fit line and different smoothings

In statistics,signal processing,econometrics andmathematical finance, a time series is a sequence ofdata points,measured typically at successive times spaced at uniform time intervals. Examples of time series are the dailyclosing value of the Dow Jones index or the annual flow volume of the Nile River at Aswan. Time series analysiscomprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of

the data. Time seriesforecastingis the use of amodelto forecast future events based on known past events topredict data points before they are measured. Time series are very frequently plotted via line charts.

Time series data have a natural temporal ordering. This makes time series analysis distinct from other common dataanalysis problems, in which there is no natural ordering of the observations (e.g. explaining people's wages byreference to their education level, where the individuals' data could be entered in any order). Time series analysis isalso distinct fromspatial data analysiswhere the observations typically relate to geographical locations (e.g.accounting for house prices by the location as well as the intrinsic characteristics of the houses). A time series modelwill generally reflect the fact that observations close together in time will be more closely related than observationsfurther apart. In addition, time series models will often make use of the natural one-way ordering of time so thatvalues for a given period will be expressed as deriving in some way from past values, rather than from future values(seetime reversibility.)

Methods for time series analyses may be divided into two classes:frequency-domain methods andtime-domainmethods. The former include spectral analysisand recentlywavelet analysis; the latter includeauto-correlation and

cross-correlationanalysis.

Contents

[hide]

1 Analysis

1.1 General exploration

1.2 Description

1.3 Prediction and

forecasting

2 Models

2.1 Notation

2.2 Conditions

2.3 Models

3 Related tools

4 See also
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5 References

6 Further reading

7 External links

[edit] Analysis

There are several types of data analysis available for time series which are appropriate for different purposes.

[edit] General exploration

Graphical examination of data series

Autocorrelation analysis to examineserial dependence

Spectral analysis to examine cyclic behaviour which need not be related toseasonality. For example, sun spotactivity varies over 11 year cycles.[1][2]Other common examples include celestial phenomena, weather patterns,neural activity, commodity prices, and economic activity.

[edit] Description

Separation into components representing trend, seasonality, slow and fast variation, cyclical irregular: seedecomposition of time series

Simple properties ofmarginal distributions

[edit] Prediction and forecasting

Fully formed statistical models forstochastic simulation purposes, so as to generate alternative versions of thetime series, representing what might happen over non-specific time-periods in the future

Simple or fully formed statistical models to describe the likely outcome of the time series in the immediatefuture, given knowledge of the most recent outcomes (forecasting).

[edit] Models

Models for time series data can have many forms and represent different stochastic processes. When modelingvariations in the level of a process, three broad classes of practical importance are theautoregressive(AR) models,the integrated(I) models, and the moving average(MA) models. These three classes depend linearly[3] on previousdata points. Combinations of these ideas produce autoregressive moving average(ARMA) and autoregressive

integrated moving average (ARIMA) models. Theautoregressive fractionally integrated moving average (ARFIMA)model generalizes the former three. Extensions of these classes to deal with vector-valued data are available underthe heading of multivariate time-series models and sometimes the preceding acronyms are extended by including aninitial "V" for "vector". An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have a causal effect on the observed series): thedistinction from the multivariate case is that the forcing series may be deterministic or under the experimenter'scontrol. For these models, the acronyms are extended with a final "X" for "exogenous".

Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibilityof producing a chaotic time series. However, more importantly, empirical investigations can indicate the advantageof using predictions derived from non-linear models, over those from linear models, as for example innonlinearautoregressive exogenous models.

Among other types of non-linear time series models, there are models to represent the changes of variance alongtime (heteroskedasticity). These models represent autoregressive conditional heteroskedasticity (ARCH) and the

collection comprises a wide variety of representation (GARCH, TARCH, EGARCH, FIGARCH, CGARCH, etc).Here changes in variability are related to, or predicted by, recent past values of the observed series. This is incontrast to other possible representations of locally varying variability, where the variability might be modelled as

being driven by a separate time-varying process, as in a doubly stochastic model.

In recent work on model-free analyses, wavelet transform based methods (for example locally stationary waveletsand wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution)techniques decompose a given time series, attempting to illustrate time dependence at multiple scales.

[edit] Notation
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A number of different notations are in use for time-series analysis. A common notation specifying a time seriesXthat is indexed by the natural numbers is written

X= {X1,X2, ...}.

Another common notation is

Y= {Yt: tT},

where Tis theindex set.

[edit] Conditions

There are two sets of conditions under which much of the theory is built:

Stationary process

Ergodicity

However, ideas ofstationarity must be expanded to consider two important ideas:strict stationarity andsecond-order stationarity. Both models and applications can be developed under each of these conditions,although the models in the latter case might be considered as only partly specified.

In addition, time-series analysis can be applied where the series are seasonally stationaryor non-stationary.Situations where the amplitudes of frequency components change with time can be dealt with intime-frequency analysis which makes use of atimefrequency representation of a time-series or signal.[4]

[edit] Models

Main article:Autoregressive model

The general representation of an autoregressive model, well-known as AR(p), is

where the term t is the source of randomness and is calledwhite noise. It is assumed to have thefollowing characteristics:

With these assumptions, the process is specified up to second-order moments and,subject to conditions on the coefficients, may be second-order stationary.

If the noise also has a normal distribution, it is called normal or Gaussian white noise.In this case, the AR process may bestrictly stationary, again subject to conditions onthe coefficients.

Scatter plotFrom Wikipedia, the free encyclopedia(Redirected from Scatter diagram)


Scatter plot
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One of theSeven Basic Tools of Quality

First described by Francis Galton

Purpose To identify the type of relationship (if any)

between two variables

Waiting time between eruptions and the duration of the eruption for theOld Faithful Geyserin YellowstoneNational Park,Wyoming, USA. This chart suggests there are generally two "types" of eruptions: short-wait-short-duration, and long-wait-long-duration.
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A 3D scatter plot allows for the visualization of multivariate data of up to four dimensions. The Scatter plot takesmultiple scalar variables and uses them for different axes in phase space. The different variables are combined to

form coordinates in the phase space and they are displayed using glyphs and colored using another scalar variable.[1]

A scatter plot orscattergraph is a type ofmathematical diagram usingCartesian coordinates to display values fortwovariablesfor a set of data.

The data is displayed as a collection of points, each having the value of one variable determining the position on thehorizontal axis and the value of the other variable determining the position on the vertical axis.[2] This kind ofplotisalso called ascatter chart,scattergram,scatter diagram orscatter graph.

Contents

[hide]

1 Overview

2 Example

3 See also

4References

5 Externallinks

Overview

A scatter plot is used when a variable exists that is under the control of the experimenter. If a parameter exists that issystematically incremented and/or decremented by the other, it is called the control parameterorindependentvariableand is customarily plotted along the horizontal axis. The measured ordependent variable is customarily

plotted along the vertical axis. If no dependent variable exists, either type of variable can be plotted on either axisand a scatter plot will illustrate only the degree ofcorrelation(notcausation) between two variables.

A scatter plot can suggest various kinds of correlations between variables with a certainconfidence interval.Correlations may be positive (rising), negative (falling), or null (uncorrelated). If the pattern of dots slopes fromlower left to upper right, it suggests a positive correlationbetween the variables being studied. If the pattern of dotsslopes from upper left to lower right, it suggests a negative correlation. A line ofbest fit(alternatively called'trendline') can be drawn in order to study the correlation between the variables. An equation for the correlation

between the variables can be determined by established best-fit procedures. For a linear correlation, the best-fitprocedure is known aslinear regressionand is guaranteed to generate a correct solution in a finite time. Nouniversal best-fit procedure is guaranteed to generate a correct solution for arbitrary relationships. A scatterplot is also very useful when we wish to see how two comparable data sets agree with each other. In this case,
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an identity line, i.e., ay=xline, or an 1:1 line, is often drawn as a reference. The more the two data sets agree,the more the scatters tend to concentrate in the vicinity of the identity line; if the two data sets arenumerically identical, the scatters fall on the identity line exactly.

One of the most powerful aspects of a scatter plot, however, is its ability to show nonlinear relationships betweenvariables. Furthermore, if the data is represented by a mixture model of simple relationships, these relationships will

be visually evident as superimposed patterns.

The scatter diagram is one of theseven basic toolsofquality control.[3]

[edit] Example

For example, to display values for "lung capacity" (first variable) and how long that person could hold his breath, aresearcher would choose a group of people to study, then measure each one's lung capacity (first variable) and howlong that person could hold his breath (second variable). The researcher would then plot the data in a scatter plot,assigning "lung capacity" to the horizontal axis, and "time holding breath" to the vertical axis.

A person with a lung capacity of 400 ml who held his breath for 21.7 seconds would be represented by a single doton the scatter plot at the point (400, 21.7) in the Cartesian coordinates. The scatter plot of all the people in the studywould enable the researcher to obtain a visual comparison of the two variables in the data set, and will help todetermine what kind of relationship there might be between the two variables.

Bar chartFrom Wikipedia, the free encyclopedia(Redirected from Bar diagram)

Jump to:navigation,searchSee also:Histogram

Example of a bar chart, with 'Country' as the discrete data set.

A bar chart orbar graph is a chart with rectangularbars with lengths proportional to the values that they represent.The bars can be plotted vertically or horizontally.

Bar charts are used for plotting discrete (or 'discontinuous') data which has discrete values and is not continuous.Some examples of discontinuous data include 'shoe size' or 'eye colour', for which you would use a bar chart. Incontrast, some examples of continuous data would be 'height' or 'weight'. A bar chart is very useful if you are tryingto record certain information whether it is continuous or not continuous data. Bar charts also look a lot like ahistogram.They are often mistaken for each other.
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