Pie Chart Article

8/21/2019 Pie Chart Article

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Pie chart

From Wikipedia, the free encyclopedia

A pie chart (or a circle graph) is acircularchart divided intosectors,illustrating

proportion. In a pie chart, thearc length of each sector (and consequently itscentral

angle andarea), isproportional to the quantity it represents. When angles are

measured with 1turn as unit then a number of percent is identified with the same

number of centiturns. Together, the sectors create a full disk. It is named for its

resemblance to apie which has been sliced. The earliest known pie chart is generally

credited toWilliam Playfair's Statistical Breviaryof 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 been criticized,[4]

and some recommend avoiding

it[5][6][7]

,pointing out in particular that it is difficult to compare different sections of a given

pie chart, or to compare data across different pie charts. Pie charts can be an effective

way of displaying information in some cases, in particular if the intent is to compare the

size of a slice with the whole pie, rather than comparing the slices among them.[1]

Pie

charts work particularly well when the slices represent 25 to 50% of the data,[8]but in

general, other plots such as thebar chart or thedot plot,or non-graphical methods such

astables,may be more adapted for representing certain information.It also shows the

frequency within certain groups of information

Example

The following example chart is based on preliminary results of theelection for the

European Parliament in 2004.The table lists the number of seats allocated to each

party group, along with the derived percentage of the total that they each make up. The

values in the last column, the derived central angle of each sector, is found by

multiplying the percentage by 360.
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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 7.4

ELDR 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 of the central angles has to be 360, the

central angle for a quantity that is a fraction Qof the total is 360Qdegrees. 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 one decimal place(s), equals 135.7.
http://en.wikipedia.org/wiki/European_United_Left%E2%80%93Nordic_Green_Lefthttp://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%27s_Partyhttp://en.wikipedia.org/wiki/Union_for_Europe_of_the_Nationshttp://en.wikipedia.org/wiki/Union_for_Europe_of_the_Nationshttp://en.wikipedia.org/wiki/European_People%27s_Partyhttp://en.wikipedia.org/wiki/European_Liberal_Democrat_and_Reform_Partyhttp://en.wikipedia.org/wiki/Europe_of_Democracies_and_Diversitieshttp://en.wikipedia.org/wiki/European_Free_Alliancehttp://en.wikipedia.org/wiki/Party_of_European_Socialistshttp://en.wikipedia.org/wiki/European_United_Left%E2%80%93Nordic_Green_Left


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[edit]Use, effectiveness and visual perception

Three sets ofdata plotted using pie charts and bar charts.

Pie charts are common in business and journalism, perhaps because they are

perceived as being less "geeky" than other types of graph. Howeverstatisticians

generally regard pie charts as a poor method of displaying information, and they are

uncommon in scientific literature. One reason is that it is more difficult for comparisons

to be made between the size of items in a chart when area is used instead of length and

when different items are shown as different shapes.Stevens' power law states that

visual area is perceived with a power of 0.7, compared to a power of 1.0 for length. This

suggests that length is a better scale to use, since perceived differences would be

linearly related to actual differences.

Further, in research performed atAT&T Bell Laboratories,it was shown that comparison

by angle was less accurate than comparison by length. This can be illustrated with the

diagram to the right, showing three pie charts, and, below each of them, the

corresponding bar chart representing the same data. Most subjects have difficultyordering the slices in the pie chart by size; when the bar chart is used the comparison is

much easier.[9].Similarly, comparisons between data sets are easier using the bar chart.

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 and the multiple is close to 25 or 50 percent, then a pie chart

can often be more effective than a bar graph.
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Line graph


This article is about the mathematical concept. For statistical presentation method, see

line chart.

Ingraph theory,the line graph L(G) of anundirected graph Gis another graph L(G) that

represents the adjacencies betweenedges of G. The name line graph comes from a

paper byHarary & Norman (1960) although bothWhitney (1932) andKrausz (1943)

used the construction before this.[1]Other terms used for the line graph include edge

graph, the theta-obrazom, the covering graph, the derivative, the edge-to-vertex dual,

the interchange graph, the adjoint, the conjugate, the derived graph, and therepresentative graph.[2]

One of the earliest and most important theorems about line graphs is due toHassler

Whitney (1932), who proved that with one exceptional case the structure of Gcan be

recovered completely from its line graph. In other words, with that one exception, the

entire graph can be deduced from knowing the adjacencies of edges ("lines").

Given a graph G, its line graph L(G) is a graph such that

eachvertex of L(G) represents an edge of G; and

two vertices of L(G) are adjacent if and only if their corresponding edges share a

common endpoint ("areadjacent") in G.

That is, it is theintersection graph of the edges of G, representing each edge by the set

of its two endpoints.

Example construction

The following figures show a graph (left, with blue vertices) and its line graph (right, with

green vertices). Each vertex of the line graph is shown labeled with the pair of endpoints

of the corresponding edge in the original graph. For instance, the green vertex on the
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right labeled 1,3 corresponds to the edge on the left between the blue vertices 1 and 3.

Green vertex 1,3 is adjacent to three other green vertices: 1,4 and 1,2 (corresponding to

edges sharing the endpoint 1 in the blue graph) and 4,3 (corresponding to an edge

sharing the endpoint 3 in the blue graph).

Graph G

Vertices in L(G) constructed

from edges in G

Added edges in

L(G)

The line graph

L(G)

[edit]Line graphs of convex polyhedra

A source of examples from geometry are the line graphs of the graphs ofsimple

polyhedra.Taking the line graph of the graph of thetetrahedron one gets the graph of

theoctahedron;from the graph of thecube one gets the graph of acuboctahedron;from

the graph of thedodecahedron one gets the graph of theicosidodecahedron,etc.

Geometrically, the operation consists in cutting each vertex of the polyhedron with a

plane cutting all edges adjacent to the vertex at their midpoints; it is sometimes named

rectification.

If a polyhedron is not simple (it has more than three edges at a vertex) the line graph

will be nonplanar, with aclique replacing each high-degree vertex. Themedial graph is

a variant of the line graph of a planar graph, in which two vertices of the medial graph

are adjacent if and only if the corresponding two edges are consecutive on some face ofthe planar graph. For simple polyhdera, the medial graph and the line graph coincide,

but for non-simple graphs the medial graph remains planar. Thus, the medial graphs of

the cube and octahedron are both isomorphic to the graph of the cuboctahedron, and

the medial graphs of the dodecahedron andicosahedron are both isomorphic to the

graph of the icosidodecahedron.
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Properties

Properties of a graph Gthat depend only on adjacency between edges may be

translated into equivalent properties in L(G) that depend on adjacency between vertices.

For instance, amatching in Gis a set of edges no two of which are adjacent, and

corresponds to a set of vertices in L(G) no two of which are adjacent, that is, an

independent set.

Thus,

The line graph of aconnected graph is connected. If Gis connected, it contains a

path connecting any two of its edges, which translates into a path in L(G)

containing any two of the vertices of L(G). However, a graph Gthat has some

isolated vertices, and is therefore disconnected, may nevertheless have a

connected line graph.

Amaximum independent set in a line graph corresponds tomaximum matching

in the original graph. Since maximum matchings may be found in polynomial time,

so may the maximum independent sets of line graphs, despite the hardness of

the maximum independent set problem for more general families of graphs.

Theedge chromatic number of a graph Gis equal to thevertex chromaticnumber of its line graph L(G).

The line graph of anedge-transitive graph isvertex-transitive.

If a graph Ghas anEuler cycle,that is, if Gis connected and has an even

number of edges at each vertex, then the line graph of GisHamiltonian.

(However, not all Hamiltonian cycles in line graphs come from Euler cycles in this

way.)

Line graphs areclaw-free graphs,graphs without aninduced subgraph in the

form of a three-leaf tree.
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Characterization and recognition

The nine minimal non-line graphs, from Beineke's forbidden-subgraph characterization

of line graphs. A graph is a line graph if and only if it does not contain one of these nine

graphs as an induced subgraph.

A graph Gis the line graph of some other graph, if and only if it is possible to find a

collection ofcliques in G, partitioning the edges of G, such that each vertex of G

belongs to at most two of the cliques. In order to do this, it may be necessary for some

of the cliques to be single vertices. By the result ofWhitney (1932),[3]

if Gis not a

triangle, there can be only one partition of this type. If such a partition exists, we can

recover the original graph for which Gis a line graph, by creating a vertex for each

clique, and connecting two cliques by an edge whenever Gcontains a vertex belonging

to both cliques. Therefore, except for the case of K3and K1,3, if the line graphs of two

connected graphs areisomorphic then the graphs are isomorphic.Roussopoulos (1973)

used this observation as the basis for a linear time algorithm for recognizing line graphs

and reconstructing their original graphs.
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Scatter Plot

Definition of Scatter Plot

A scatter plot is a graph made by plotting ordered pairs in a coordinate plane to

show the correlation between two sets of data.

More about Scatter Plot

A scatter plot describes a positive trend if, as one set of values increases, the

other set tends to increase.

A scatter plot describes a negative trend if, as one set of values increases, the

other set tends to decrease.

A scatter plot shows no trend if the ordered pairs show no correlation.

Examples of Scatter Plot

The scatter plot shows the hours of study and test scores of 20 students.

As the number of hours of study increases, the marks scored tend to increase.

So, the scatter plot describes a positive trend.

Solved Example on Scatter Plot

Emily measured the depth of water in a bathtub at two-

minute intervals after the tap was turned on. The table

shows her data. Make a scatter plot for the data.

Time (in minutes) Depth (in cm)

2 74 8

6 13

8 19

10 20

12 24


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14 32

16 37

18 38

20 41

22 47

Choices:

A. Graph 2

B. Graph 1

C. Graph 3

D. Graph 4

Correct Answer: B

Solution:

Step 1: In a graph paper,

represent the time in minutes

along the x-axis and the

depth of water in the bathtub

along the y-axis.

Step 2: Plot the values in the table. The

scatter plot would look like the one below.

Step 3: Graph 4 matches the given data.

Related Terms for Scatter Plot

Ordered pair

Coordinate plane Correlation

Graph

Data


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Bar chart


Jump to:navigation,search

See also:Histogram

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

A bar chart or bar graph is achart withrectangular bars withlengths proportional to the

values that they represent. The bars can also be plotted horizontally.

Bar charts are used for plotting discrete (or 'discontinuous') data i.e. 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. In contrast, some

examples of continuous data would be 'height' or 'weight'. A bar chart is very useful if

you are trying to record certain information whether it is continuous or not continuous

data.
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Example

The following table lists the number of seats allocated to each party group in European

elections in 1999 and 2004. The results of 1999 have been multiplied by 1.16933, to

compensate for the change in number of seats between those years. Sometimes it can

be horizontal.

This bar chart shows both the results of 2004, and those of 1999:


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Histogram


Instatistics,a histogram is agraphical display of tabularfrequencies,shown as

adjacentrectangles.Each rectangle is erected over an interval, with an area equal to

the frequency of the observations in the interval. The height of a rectangle is also equal

to the frequency density of the interval, i.e., the frequency divided by the width of the

interval. The total area of the histogram is equal to the number of data. A histogram may

also be based on relative frequencies. It then shows the proportion of cases that fall into

each of severalcategories,with the total area equaling 1. The categories are usually

specified as consecutive, non-overlappingintervals of a variable. The categories(intervals) must be adjacent, and often are chosen to be of the same size .[1]

Histograms are used to plot density of data, and often fordensity estimation:estimating

theprobability density function of the underlying variable. The total area of a histogram

used for probability density is always normalized to 1. If the length of the intervals on the

x-axis are all 1, then a histogram is identical to arelative frequency plot.

An alternative to the histogram iskernel density estimation,which uses akernel tosmooth samples. This will construct asmooth probability density function, which will in

general more accurately reflect the underlying variable.

The histogram is one of the seven basic tools ofquality

control.

Examples

As an example we consider data collected by theU.S.

Census Bureau on time to travel to work (2000 census,

[1],Table 2). The census found that there were 124

million people who work outside of their homes. An

interesting feature of this graph is that the number recorded for "at least 15 but less than
http://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Graphical_displayhttp://en.wikipedia.org/wiki/Frequency_%28statistics%29http://en.wikipedia.org/wiki/Rectanglehttp://en.wikipedia.org/wiki/Categorizationhttp://en.wikipedia.org/wiki/Interval_%28mathematics%29http://en.wikipedia.org/wiki/Histogram#cite_note-0http://en.wikipedia.org/wiki/Histogram#cite_note-0http://en.wikipedia.org/wiki/Histogram#cite_note-0http://en.wikipedia.org/wiki/Density_estimationhttp://en.wikipedia.org/wiki/Probability_density_functionhttp://en.wikipedia.org/wiki/Relative_frequencyhttp://en.wikipedia.org/wiki/Kernel_density_estimationhttp://en.wikipedia.org/wiki/Kernel_%28statistics%29http://en.wikipedia.org/wiki/Smooth_functionhttp://en.wikipedia.org/wiki/Quality_controlhttp://en.wikipedia.org/wiki/Quality_controlhttp://en.wikipedia.org/wiki/United_States_Census_Bureauhttp://en.wikipedia.org/wiki/United_States_Census_Bureauhttp://www.census.gov/prod/2004pubs/c2kbr-33.pdfhttp://en.wikipedia.org/wiki/File:Black_cherry_tree_histogram.svghttp://www.census.gov/prod/2004pubs/c2kbr-33.pdfhttp://en.wikipedia.org/wiki/United_States_Census_Bureauhttp://en.wikipedia.org/wiki/United_States_Census_Bureauhttp://en.wikipedia.org/wiki/Quality_controlhttp://en.wikipedia.org/wiki/Quality_controlhttp://en.wikipedia.org/wiki/Smooth_functionhttp://en.wikipedia.org/wiki/Kernel_%28statistics%29http://en.wikipedia.org/wiki/Kernel_density_estimationhttp://en.wikipedia.org/wiki/Relative_frequencyhttp://en.wikipedia.org/wiki/Probability_density_functionhttp://en.wikipedia.org/wiki/Density_estimationhttp://en.wikipedia.org/wiki/Histogram#cite_note-0http://en.wikipedia.org/wiki/Interval_%28mathematics%29http://en.wikipedia.org/wiki/Categorizationhttp://en.wikipedia.org/wiki/Rectanglehttp://en.wikipedia.org/wiki/Frequency_%28statistics%29http://en.wikipedia.org/wiki/Graphical_displayhttp://en.wikipedia.org/wiki/Statistics


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20 minutes" is higher than for the

bands on either side. This is likely to

have arisen from people rounding

their reported journey time. This

rounding is a common phenomenon

when collecting data from people.

Histogram of travel time, US 2000

census. Area under the curve

equals the total number of cases. This diagram uses Q/width from the table.

Data by absolute numbers

Interval Width Quantity Quantity/width

0 5 4180 836

5 5 13687 2737

10 5 18618 3723

15 5 19634 3926

20 5 17981 3596

25 5 7190 1438

30 5 16369 3273

35 5 3212 642

40 5 4122 824

45 15 9200 613
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60 30 6461 215

90 60 3435 57

This histogram shows the number of cases perunit interval so that the height of each

bar is equal to the proportion of total people in the survey who fall into that category.

The area under the curve represents the total number of cases (124 million). This type

of histogram shows absolute numbers.

Histogram of travel time, US 2000

census. Area under the curve

equals 1. This diagram uses

Q/total/width from the table.

Data by proportion

Interval Width Quantity (Q) Q/total/width

0 5 4180 0.0067

5 5 13687 0.0221

10 5 18618 0.0300

15 5 19634 0.0316

20 5 17981 0.0290

25 5 7190 0.0116
http://en.wikipedia.org/wiki/Unit_intervalhttp://en.wikipedia.org/wiki/File:Travel_time_histogram_total_1_Stata.pnghttp://en.wikipedia.org/wiki/File:Travel_time_histogram_total_1_Stata.pnghttp://en.wikipedia.org/wiki/File:Travel_time_histogram_total_1_Stata.pnghttp://en.wikipedia.org/wiki/File:Travel_time_histogram_total_1_Stata.pnghttp://en.wikipedia.org/wiki/Unit_interval


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30 5 16369 0.0264

35 5 3212 0.0052

40 5 4122 0.0066

45 15 9200 0.0049

60 30 6461 0.0017

90 60 3435 0.0005

This histogram differs from the first only in thevertical scale. The height of each bar is

the decimal percentage of the total that each category represents, and the total area of

all the bars is equal to 1, the decimal equivalent of 100%. The curve displayed is a

simpledensity estimate.This version shows proportions, and is also known as a unit

area histogram.

In other words, a histogram represents a frequency distribution by means of rectangles

whose widths represent class intervals and whose areas are proportional to the

corresponding frequencies. The intervals are placed together in order to show that the

data represented by the histogram, while exclusive, is also continuous. (E.g., in a

histogram it is possible to have two connecting intervals of 10.5-20.5 and 20.5-33.5, but

not two connecting intervals of 10.5-20.5 and 22.5-32.5. Empty intervals are

represented as empty and not skipped.)
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Pictograph

http://www.tutorvista.com/math/math-pictographs

Introduction for Math Pictographs:

In math, graph is a representation of data by means of diagrams. There are various

types of graphs. The basic type of representation of data is a pictograph. The

representation of data by means of pictures are said to be pictograph. In this article we

shall discuss about pictographs in math. Also we shall draw sample pictographs in math.

How to Draw a Pictograph in Math:

Pictograph is a method of representing statistical data by means of symbolic facts to

competition the frequencies of different kinds of data. Basically, the pictographs are very

interactive for the students to study data easily.

Let us draw a pictograph to represent the students who are playing different games in a

school.

There are 650 students in a school. There are 4 types of games that the school is

affording. They are Baseball, basket ball, rugby and soccer.

There are 140 students who are playing baseball.

There are 120 students who are playing basket ball.

There are 220 students who are playing rugby.

There are 170 students playing soccer.
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The pictogram for the given data in shown below:

In this pictograph, we can

see the different types of

games are represented with

different pictures. The

representation like this are

said to be pictographs.

The pictographs are very

similar to histograms. In

histograms, we represent

data by means of bars, while

in pictograph; we use pictures in the place of bar graphs.

Example for Pictogram in Math:

Draw a pictograph to represents variety of apples available in super market.

Solution:

In this pictograph, there are 30 Red

Delicious apples available in the

supermarket.

There are 25 Golden Delicious

apples available in the super market.

There are 40 Red Rome apples

available in the super market.

There are 20 McIntosh variety

of apples are available in the super

market.

There are 35 Jonathan apples

available in the super market.

So, the total number of apples in the

super market is 30 + 25 + 40 + 20 +

35 = 150

There are totally 150 apples available in the super market.

Documents

Pie Chart Article