Key vocabulary identified at the beginning of each lesson.
Thedatacouldalsobeshowninadotplot(below).
Refined language supports students with lower literacy levels.
Lesson starter activities may be adapted from the mainstream Essential Mathematics series, with questions modified to better meet the specific needs of students.
■ A dot plot can be used to display discrete numerical data, where each dot represents one datum.
■ A column graph is a way to show data in different categories, and is useful when more than a few items of data are present.
■ Column graphs can be drawn vertically or horizontally. Horizontal column graphs are sometimes also called bar graphs.
■ Graphs should have the following features:
A title explaining what the graph is about
Category labels for any non-numerical data
■ Any numerical axis must be drawn to scale.
■ An outlier is a value that is noticeably distinct from the main cluster of points.
■ Data represented as a dot plot could be described as symmetrical or skewed (or neither).
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8C Column graphs and dot plots
ESSENTIAL MATHEMATICS CORE
FOR THE AUSTRALIAN CURRICULUM SECOND EDITION
Keyideas
A dotplot isagraphthatcanbeusedtodisplaydata,whereeachdotrepresentsone datum
A columngraph isagoodwaytoshowdataindifferentcategories,andisusefulwhenmorethan afewitemsofdataarepresent.Columngraphscanbedrawnvertically(goingup)orhorizontally (goingacross).
Graphsshouldhavethefollowingfeatures:
A title explaining what the graph is about
labels for any non-numerical data
An outlier isavaluethatisnoticeablysmallerorlargerthanthemainclusterofpoints.
Fewer Key ideas are covered, to focus on helping students meet the minimum requirements of the Achievement Standards.
1 Fillintheblanksinthefollowingsentences.
a A isagraphwhichusesdotstorepresentdata.
b Agraphshowingdataindifferentcategoriesasrectanglesiscalleda
c An isavaluethatisnoticeablysmallerorlargerthanthemainclusterofpoints.
Understanding questions are closely linked to the Key ideas section to promote class discussion and to help consolidate the fundamental skills and concepts needed for the topic.
ESSENTIAL MATHEMATICS
First decide which scale goes on the vertical axis.
Maximum height = 150 cm, so axis goes from 0 cm to 160 cm (to allow a bit above the highest value).
Remember to include all the features required, including axes labels and a graph title.
Now you try
Draw a column graph to represent the following people’s arm spans.
Name MattPatCarlyKimTristan
Exercise 8C
1 The dot plot on the right represents the results of a survey that asked some people how many times they had flown overseas.
a Use the graph to state how many people have flown overseas once.
b How many people participated in the survey?
c What is the range of values?
d What is the median number of times flown overseas?
e What is the outlier?
f What is the mode?
2 In a Year 4 class, the results of a spelling quiz are presented as a dot plot.
b Whatistherangeofvalues? c Whatisthemediannumberofpets?
d Whatistheoutlier? e Whatisthemode? f
Solution
a 4 children
b 15 children
c 8−0 = 8
Worked examples are carefully selected to suit the needs of this cohort and often contain fewer new skills in each example. They appear in the exercises directly above the related questions.
Explanation
Thereare 4 dotsinthe‘2 pets’category, so 4 childrenhave 2 pets.
Thetotalnumberofdotsis 15
Range = highest lowest Inthiscase,highest = 8,lowest = 0
d Give a reason why the number of people driving to work has decreased.
e What is one other trend that you can see from looking at this graph?
ESSENTIAL MATHEMATICS
7 a Draw a column graph to show the results of the following survey of the number of male and female puppies sold by a commercial dog breeder. Put time (years) on the horizontal axis.
FOR THE AUSTRALIAN CURRICULUM FOURTH EDITION
b During which year(s) were there more female puppies sold than male puppies?
c Which year had the fewest number of puppies sold?
d Which year had the greatest number of puppies sold?
e During the entire period of the survey, were there more male or female puppies sold?
PROBLEM-SOLVING
9 A survey is conducted of students’ favourite subjects from a choice of Art, Maths, English, History and Science. Someone has attempted to depict the results in a column graph.
8 The average (mean) income of adults in a particular town is graphed over a 6-year period.
a What is wrong with the scale on the vertical axis?
b Give at least two other problems with this graph.
a Describe in one sentence what has happened to the income over this period of time.
b Estimate what the average income in this town might have been in 2012
c Redraw the graph with an even scale and appropriate labels.
c Estimate what the average income might be in 2028 if this trend continues.
d The original graph makes Maths look twice as popular as Art, based on the column size.
According to the survey, how many times more popular is Maths?
e The original graph makes English look three times as popular as Maths. According to the survey, how much more popular is English?
f Assume that Music is now added to the survey’s choice of subjects. Five students who had previously chosen History now choose Music, and 16 students who had previously chosen English now choose Music. What is the most popular subject now?
10 Mr Martin and Mrs Stevensson are the two Year 3 teachers at a school. For the latest arithmetic quiz, they have plotted their students’ scores on a special dot plot called a parallel dot plot, shown opposite.
a What is the median score for class 3M?
b What is the median score for class 3S?
c State the range of scores for each class.
d Based on this test, which class has a greater spread of arithmetic abilities?
e If the two classes competed in an arithmetic competition, where each class is allowed only one representative, which class is more likely to win? Justify your answer. REASONING
11 At a central city train station, three types of services run – local, country and interstate. The average number of passenger departures during each week is shown in the stacked column graph.
a Approximately how many passenger departures per week were there in 2013?
b Approximately how many passenger departures were there in total during 2018?
c Does this graph suggest that the total number of passenger departures has increased or decreased during the period 2013–2018?
d Approximately how many passengers departed from this station in the period 2013–2018? Explain your method clearly and try to get your answer within 10 000 of the actual number.
ESSENTIAL MATHEMATICS CORE
FOR THE AUSTRALIAN CURRICULUM
12 a Drawacolumngraphtoshowtheresultsofthefollowingsurveyofthenumberofmalesand femalesbornatacertainhospital.Puttheyearsonthehorizontalaxis.
b Duringwhichyear(s)weremorefemalesbornthanmales?
c Whichyearhadthesmallestnumberofbirths?
d Whichyearhadthegreatestnumberofbirths?
e Duringthetimeofthesurvey,weremoremalesorfemalesborn?
