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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

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The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
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Q2 x+(x+2)+(x+4)=60 3x+6=60 3x+6-6=60-6 3x=54 3x/3=54/3 x=18 :. The numbers are 18,20 and 22
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
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Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
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x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
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Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Need help solving this problem (2/7)^-2
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A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
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Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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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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