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Graphical Representation of Data

Graphical Representation of Data

Introduction



  • Any data before they are analyzed by statistical methods have to be arranged

    and displayed in a manner that is informative and attractive. Tabular representation

    is one form of doing it. But for those who do not have an affinity for numbers, tables

    are not as attractive. Graphic or diagrammatic presentation of data adds a pictorial

    effect to what would otherwise be just a mass of figures. A major advantage of these

    representations is that they have more appeal especially to a layman as they communicate

    information visually. For this reason graphs are often used in newspapers, magazines

    and businesses around the world. As features of data become visible at a glance in a graph,

    one can study easily the fluctuation of data and hence know the correlation between two or

    more sets of data, which in turn helps in forecasting.


Commonly used forms



    The important aspects include providing a self-explanatory title, size and proportion, color

    shades, necessary footnotes, source table and the index. The most commonly used graphical or

    diagrammatical forms for representation of data are: -

  • Pictograph


  • Stem-and-Leaf Plot


  • Line graph


  • Bar Graph


  • Circle Graph


  • Box and Whisker Plot


  • Histogram


  • Frequency polygon


  • Ogive curve


Pictograph



    This is a very common diagram used by advertisers in which appropriate pictures are drawn with

    sizes proportional to the magnitudes of the observations.




Example of Pictograph



    The pictograph shows the number of varieties of apples stored at a supermarket.

    From the pictograph it can be understood that the number of Red Delicious apples stored is 30.






Stem-and-Leaf Plot



    The stem-and-leaf plot is used to plot the frequency with which certain classes of values occur

    It is an arrangement used to display numerical data in order.




Example of a Stem-and-Leaf plot:



    This stem-and-leaf plot shows the number of shrubs collected by each student

    The stem-and-leaf plot shows that two students have collected equal number of shrubs, that is 21.








Line graph



    This graph shows the data against time, which could be of any measure such as hours, days, weeks, months or years.





Example of a Line graph:



    This line graph shows the circulation of a magazine (in thousands) in the first quarter of a year.

    In the second quarter of the year the circulation of the magazine was 100,000.








Bar graph



    A bar graph is a pictorial representation of numerical data, which makes use of a number of rectangular bars of uniform width with equal spacing between them. A bar graph is appropriate for comparing data in which observations corresponds to different categories.


Example of a Bar graph:



    This bar graph displays the number of birthdays of students in each month.

    As per the bar graph, birthday of 4 students fall in the month of February.






Circle graph (Pie chart)



    This graph is drawn using circle with areas proportional to the magnitudes of the observations.

    Circle graphs are generally used to represent data as a part of whole.




Example of a Circle graph:



    This circle graph displays the annual expenditure of a software company

    The circle graph shows that the annual expenditure of the software company for

    education & training is $20 millions.






Box-and-Whisker Plot



    Box-and-whisker plots depict the smallest observation, lower quartile, median, upper

    quartile and largest observation of a given data. They even help in identifying the

    outlier of the given set of data.




Example of a Box-and-Whisker plot:



    The following table shows the heights of mountains in U.S.












Example of a Box-and-Whisker plot:



    The box-and-whisker plot for the given data is given below.








Histogram



    The histogram is a graphical representation of a continuous frequency distribution in which

    vertical rectangles are erected over the corresponding class intervals without leaving any gap amongst them.




Example of a Histogram:



    This histogram indicates the number of employees of a company under different age groups.










    From the graph, we can observe that the number of employees under the age group 20-24 is 5.




Frequency polygon)



    Joining the midpoints of the rectangles of a histogram by straight lines makes a frequency polygon.

    It shows the outline of a data pattern vividly.




Example of a Frequency Polygon:



    This frequency polygon shows the fluctuation in points scored by a team in a basketball game.





    The frequency polygon shows that the team had scored 3 points more frequently




Ogive curve



    The curve drawn by plotting points with the upper (lower) boundaries of classes as

    X- coordinates and the corresponding less than (greater than) frequencies as

    Y-coordinates and joining these points by a smooth curve starting from (ending at) the

    lower (upper) bound of the first (last) class is called a less than (greater than) ogive.

    These ogives enable us to know how many observations are above or below a certain value.




Example of Ogive curve:



    This ogive curve shows the distribution of the weekly wages (in $) of workers in a factory.









    The ogive curve shows that the number of workers earning weekly more than $600 is 30.


Additional Links for Graphical Representation



  • Click here for samples


  • Click here for Mathematics Dictionary




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