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Unlike histograms, many frequency polygons can be plotted together to compare several frequency distributions, provided that the data has been grouped in the same way and provide a clear way to compare multiple datasets.

Pie charts

A pie chart is a graph that is used to show what categories make up a specific section of the data, and what the contribution each category makes to the entire set of data. A pie chart is based on a circle, and each category is represented as a wedge of the circle or alternatively as a slice of the pie. The area of each wedge is proportional to the ratio of that specific category to the total number of data values in the data set. The wedges are usually shown in different colours to make the distinction between the different categories easier.

Example of a pie chart for Data Set 1. Pie charts show what contribution each group makes to the total data set.

Method: Drawing a pie-chart

  1. Draw a circle that represents the entire data set.
  2. Calculate what proportion of 360   each category corresponds to according to
    Angular Size = Frequency Total × 360
  3. Draw a wedge corresponding to the angular contribution.
  4. Check that the total degrees for the different wedges adds up to close to 360 .

Draw a pie chart for Data Set 2 , showing the relative proportions of each data value to the total.

  1. Total
    Data Value 1 2 3 4 5 6
    Frequency 30 32 35 34 37 32 200
  2. Data Value Angular Size of Wedge
    1 Frequency Total × 360 = 30 200 × 360 = 54
    2 Frequency Total × 360 = 32 200 × 360 = 57 , 6
    3 Frequency Total × 360 = 35 200 × 360 = 63
    4 Frequency Total × 360 = 34 200 × 360 = 61 , 2
    5 Frequency Total × 360 = 37 200 × 360 = 66 , 6
    6 Frequency Total × 360 = 32 200 × 360 = 57 , 6

Note that the total angular size of the wedges may not add up to exactly 360   because of rounding.

Line and broken line graphs

All graphs that have been studied until this point (bar, compound bar, histogram, frequency polygon and pie) are drawn from grouped data. The graphs that will be studied in this section are drawn from the ungrouped or raw data.

Line and broken line graphs are plots of a dependent variable as a function of an independent variable, e.g. the average global temperature as a function of time, or the average rainfall in a country as a function of season.

Usually a line graph is plotted after a table has been provided showing the relationship between the two variables in the form of pairs. Just as in (x,y) graphs, each of the pairs results in a specific point on the graph, and being a line graph these points are connected to one another by a line.

Many other line graphs exist; they all connect the points by lines, not necessarily straight lines. Sometimes polynomials, for example, are used to describe approximately the basic relationship between the given pairs of variables, and between these points.

Example of a line graph for Data Set 5.

Clawde the cat is overweight and her owners have decided to put her on a restricted eating plan. Her mass is measured once a month and is tabulated below. Draw a line graph of the data to determine whether the restricted eating plan is working.

Month Mass (kg)
March 4,53
April 4,56
May 4,51
June 4,41
July 4,41
August 4,36
September 4,43
October 4,37
  1. We are required to plot a line graph to determine whether the restricted eating plan is helping Clawde the cat lose weight. We are given all the information that we need to plot the graph.

  2. There is a slight decrease of mass from March to October, so the restricted eating plan is working, but very slowly.

Exercises - graphical representation of data

  1. Represent the following information on a pie chart.
    Walk 15
    Cycle 24
    Train 18
    Bus 8
    Car 35
    Total 100
    Click here for the solution
  2. Represent the following information using a broken line graph.
    Time 07h00 08h00 09h00 10h00 11h00 12h00
    Temp ( C) 16 16,5 17 19 20 24
    Click here for the solution
  3. Represent the following information on a histogram. Using a coloured pen, draw a frequency polygon on this histogram.
    Time in seconds Frequency
    16 - 25 5
    26 - 35 10
    36 - 45 26
    46 - 55 30
    56 - 65 15
    66 - 75 12
    76 - 85 10
    Click here for the solution
  4. The maths marks of a class of 30 learners are given below, represent this information using a suitable graph.
    82 75 66 54 79 78 29 55 68 91
    43 48 90 61 45 60 82 63 72 53
    51 32 62 42 49 62 81 49 61 60
    Click here for the solution
  5. Use a compound bar graph to illustrate the following information
    Year 2003 2004 2005 2006 2007
    Girls 18 15 13 12 15
    Boys 15 11 18 16 10
    Click here for the solution

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
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