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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

Preparation and Applications of Nanomaterial for Drug Delivery
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Application of nanotechnology in medicine
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Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
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I think
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Brian Reply
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What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
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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?
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biomolecules are e building blocks of every organics and inorganic materials.
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sciencedirect big data base
Introduction about quantum dots in nanotechnology
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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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