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10.09 Comparing data representations

Worksheet
Compare data representations
1

The grouped bar chart shows customer satisfaction ratings for different cars, broken down by gender. The top rows in each category represents males and the bottom rows represent females.

Determine whether the following statements are true or false:

a

Honda received the highest ratings.

b

Ford received the lowest ratings among Males.

c

Both genders agree on the rank order in which the cars are rated.

d

As a group, the women seem to be tougher raters; they gave lower ratings to each car than the men gave.

e

Females prefered the cars that were red.

2

Consider the three column graphs below:

a

Is the tallest person the oldest?

b

Is the heaviest person the oldest?

c

Is the heaviest person the tallest?

d

Is the youngest person the lightest?

e

Is it possible for a 10-year old to be lighter than an 8-year old?

3

Consider the following graph:

a

Which city has the highest average daily sunshine hours?

b

Which city has the month with the least average sunshine hours?

c

Which city has the greatest variation in sunshine hours over the year?

4

The graph shows how the value of an investment as it changes over time:

a

How much money was initially invested?

b

What is the value of the investment after 4 years?

c

By how much is the value of the investment growing each year?

d

How much will the investment be worth in 15 years?

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\text{Years}
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10
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14
16
\text{Value } \$
5

The line graph shows the amount of petrol (in litres) in a car’s tank during a long drive:

Given that the drive started at 8 am:

a

How much petrol was initially in the tank?

b

What happened at 9 am and 1 pm?

c

How much petrol was used between 1 pm and 5 pm?

d

To the nearest hour, when did the petrol in the tank first fall below 18 litres?

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\text{Hours}
10\text{L}
12\text{L}
14\text{L}
16\text{L}
18\text{L}
20\text{L}
22\text{L}
24\text{L}
26\text{L}
28\text{L}
30\text{L}
\text{Petrol}
6

The local library constructed divided bar graphs showing the last six months of book loans by category. Assume that the total number of loans was exactly the same for each month.

a

In which month did subscribers borrow the most business books?

b

Which month was the best month for children's books?

c

In which month did people borrow the same number of design books as environment books?

d

Which book category grew constantly during the 6 months?

e

During which month did people borrow more fiction books than environmental books?

f

During which two months did people borrow the same total number of fiction books?

7

It’s "Back to School" time and a shop recorded the number of pens they sold in one week:

a

How many pens were sold on Wednesday?

b

How many more pens were sold on Saturday than on Wednesday?

8

The graph shows the cost (in dollars) of sending parcels of various weights overseas:

a

Find the cost of sending a letter weighing 100 grams.

b

Find the cost of sending a letter weighing 300 grams.

c

What is the heaviest letter that can be sent for \$2?

50\text{ g}
100\text{ g}
150\text{ g}
200\text{ g}
250\text{ g}
300\text{ g}
\text{Weight}
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\text{Cost}
9

The graph shows the parking costs (in dollars) over different lengths of time:

a

How much would 5 hours of parking cost?

b

What is the longest you can park your car for \$6?

c

The carpark offers a weekly pass for \$44. If Aaron parks his car for 6 hours each day, five days a week, how much would he save each week with the weekly pass?

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\text{Hours}
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\text{Cost}
10

The graph represents the number of iTunes sales (in millions) and iPod sales (in hundreds of thousands) every 3 months between 2003 and 2007:

a

State the number of iTunes sales for the first quarter of 2006.

b

State the number of iPod sales for the first quarter of 2006.

c

How many more iTunes sales were there than iPod sales in the first quarter of 2007?

d

Calcuate the total number of iTunes sales in 2006.

11

The following graph shows monthly rainfall data for Berlin and London:

a

Which city records the highest monthly rainfall over the year?

b

Calculate the range in monthly rainfall for Berlin between June and October.

c

In the months between March and July (inclusive), find the range in London's monthly rainfall.

d

Which city has the lowest range over the year?

e

In which month did the cities have the smallest difference in rainfall?

12

A tree is measured every year and its height is recorded as shown in the table:

a

Based on the data given, plot a frequency polygon for the height of the tree each year.

b

Predict the height of the tree in Year 4.

\text{Year}\text{Height (cm)}
1100
2150
3190
13

Consider the following graphs:

a

Which axis measures the precipitation (rainfall), vertical or horizontal axis?

b

Which axis measures the temperature?

c

Which city has higher average temperature?

d

Which city has the higher average rainfall?

e

Determine whether the following statements are true or false:

i

The higher the average temperature in a city, the higher the average rainfall.

ii

The average minimum temperature rises with the average maximum temperature.

14

In a zoo, the most popular attractions are the elephants and zebras.

Over 3 months, the number of visitors (in hundreds) were recorded as shown in the given table:

ZebrasElephants
May2043
June2338
July2534
a

Predict the number of zebra visitors (in hundreds) in August if the pattern was to continue.

b

Predict the number of elephant visitors (in hundreds) in August if the pattern was to continue.

c

Construct a column graph to represent the number of zebra visitors each month.

d

Construct a column graph to represent the number of elephant visitors each month.

e

If the trend continues, in what month will the two animals have roughly the same number of visitors?

15

Four friends collected some data about each other and recorded them in the table below:

a

Construct a column graph depicting the students' arm spans.

b

Construct a column graph depicting the students' heights.

c

Describe the relationship between the height and arm span.

d

Describe the relationship between the height and month of birth.

NameArm spanHeightMonth of birth
\text{Homer}128\text{ cm}128\text{ cm}\text{June}
\text{Ben}138\text{ cm}136\text{ cm}\text{December}
\text{Sally}132\text{ cm}132\text{ cm}\text{June}
\text{Sophia}129\text{ cm}134\text{ cm}\text{December}
16

NOAA recorded the temperature every hour from dawn to noon in the given table:

\text{Time}\text{5 am}\text{6 am}\text{7 am}\text{8 am}\text{9 am}\text{10 am}\text{11 am}\text{12 am}
\text{Temperature }( \degree \text{C})1616171920212426

Plot a frequency polygon that represents the information in the table.

17

Derek planted some tomato seeds and two seeds sprouted. He puts Seedling A outside in the sun and Seedling B inside in the kitchen. The heights of the seedlings over time, in centimetres, are graphed below:

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\text{Weeks}
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\text{Height (cm)}
Seedling ASeedling B
Week 13 \text{ cm}
Week 22 \text{ cm}
Week 3
Week 40 \text{ cm}
Week 52 \text{ cm}
Week 6
Week 7
a

How many centimetres did Seedling A grow in the second week?

b

Complete the given table showing the increases in growth for both seedlings.

c

Which seedling appears to be growing more slowly?

d

Which conditions seem to give optimum growth for a tomato seedling?

18

The following table shows the monthly sales of two products:

MonthProduct A (number sold)Product B (number sold)
\text{January}\quad \qquad \quad \enspace 10\quad \qquad \quad \enspace 7
\text{February}\quad \qquad \quad \enspace 4\quad \qquad \quad \enspace 6
\text{March}\quad \qquad \quad \enspace 6\quad \qquad \quad \enspace 5
\text{April}\quad \qquad \quad \enspace 1\quad \qquad \quad \enspace 8
\text{May}\quad \qquad \quad \enspace 3\quad \qquad \quad \enspace 8
\text{June}\quad \qquad \quad \enspace 7\quad \qquad \quad \enspace 4
\text{July}\quad \qquad \quad \enspace 10\quad \qquad \quad \enspace 3
\text{August}\quad \qquad \quad \enspace 2\quad \qquad \quad \enspace 5
\text{September}\quad \qquad \quad \enspace 4\quad \qquad \quad \enspace 4
\text{October}\quad \qquad \quad \enspace 9\quad \qquad \quad \enspace 7
\text{November}\quad \qquad \quad \enspace 3\quad \qquad \quad \enspace 7
\text{December}\quad \qquad \quad \enspace 8\quad \qquad \quad \enspace 9

Construct a radar chart that represents the two sets of data.

19

The annual sales of two products are shown in the following radar chart:

a

How many units of Product B were sold in March?

b

How many units of Product A were sold in November?

c

How many units of Product A were sold throughout the entire year?

20

32 children took part in a survey to find out what colour they should paint the school hall. This pie chart shows their answers:

State whether the following statements are true or false:

a

Ten children like yellow best.

b

25\% of the children like green more than the other colours.

c

\dfrac{1}{5} of the children like red best.

d

Twelve children like blue best.

21

The following pie chart represents government spending:

a

What fraction is spent on Education?

b

What percentage is spent on Healthcare?

c

What percentage is spent on Defense?

22

The sector graph represents the number of people taking leave from work at a particular company:

a

If 25 people took leave in January, how many degrees represents 1 person?

b

How many people took leave in November?

c

How many people took leave between the beginning of November and the end of March?

d

What percentage took leave in December? Round your answer to two decimal places.

23

The table below shows how many of the world’s largest banks are in each country:

Number of BanksSector Angle
France\qquad \quad \enspace 4
Germany\qquad \quad \enspace 3
Japan\qquad \quad \enspace 2
United Kingdom\qquad \quad \enspace 6
United States of America\qquad \quad \enspace 9
a

So that the data can be displayed in a pie chart, complete the table by finding the angle for each country's sector.

b

Construct a pie chart to represent the information in the table.

24

The revenue generated from a company's three major products are shown in the following table:

\text{Month}\text{Product A }(\$000)\text{Product B }(\$000)\text{Product C }(\$000)
\text{January} \qquad \quad \enspace12 \qquad \quad \enspace25 \qquad \quad \enspace12
\text{February} \qquad \quad \enspace20 \qquad \quad \enspace30 \qquad \quad \enspace18
\text{March} \qquad \quad \enspace18 \qquad \quad \enspace28 \qquad \quad \enspace29
\text{April} \qquad \quad \enspace16 \qquad \quad \enspace34 \qquad \quad \enspace10
\text{May} \qquad \quad \enspace22 \qquad \quad \enspace37 \qquad \quad \enspace15
\text{June} \qquad \quad \enspace11 \qquad \quad \enspace35 \qquad \quad \enspace26
\text{July} \qquad \quad \enspace13 \qquad \quad \enspace31 \qquad \quad \enspace17
\text{August} \qquad \quad \enspace17 \qquad \quad \enspace29 \qquad \quad \enspace13
\text{September} \qquad \quad \enspace20 \qquad \quad \enspace27 \qquad \quad \enspace19
\text{October} \qquad \quad \enspace19 \qquad \quad \enspace30 \qquad \quad \enspace24
\text{November} \qquad \quad \enspace16 \qquad \quad \enspace26 \qquad \quad \enspace20
\text{December} \qquad \quad \enspace16 \qquad \quad \enspace34 \qquad \quad \enspace28

Construct a stacked area graph that represents the data.

25

Consider the following graph:

a

Do the majority of US voters believe the country is going in the right direction?

b

What percentage of US voters have an opinion on the direction the country is going in?

c

What percentage of US voters either disapprove or strongly disapprove of Obama?

d

Which of the following options is greatest?

A

The proportion of US voters whom either approve or strongly approve of Obama.

B

The proportion of US voters whom either strongly approve or strongly disapprove of Obama.

C

The proportion of US voters whom either disapprove or strongly disapprove of Obama.

26

The graph shows the impact on after-tax income under the policies of the two US presidential candidates in 2008:

Source: Washington Post

a

Under which candidate would there be tax increases for certain families?

b

What is the size of the tax cut, in dollar terms, proposed by McCain for families with income in the \$66\,355 to \$111\,645 range?

c

What is the size of the tax cut, as a percentage, proposed by Obama for families with income in the \$160\,973 to \$226\,981 range?

d

Which candidate is promising the greater average tax cut, and how much do they propose cutting it by?

e

What is the difference, in dollars, between the policies of the two candidates for the families that make up the top 0.1\% of the income scale?

27

The heat map and table below show the median house prices across various suburbs in Sydney:

SuburbMedian house price
\text{Belfield}\$975\,000
\text{Belmore}\$910\,000
\text{Burwood}\$1\,775\,000
\text{Campsie}\$1\,105\,000
\text{Croydon}\$1\,488\,000
\text{Croydon Park}\$1\,250\,000
\text{Dulwich Hill}\$1\,420\,000
\text{Earlwood}\$1\,220\,000
\text{Greenacre}\$850\,000
\text{Hurlstone Park}\$1\,253\,000
\text{Kingsgrove}\$1\,090\,000
\text{Lakemba}\$830\,000
\text{Marrickville}\$1\,285\,000
\text{Roselands}\$940\,000
\text{Strathfield}\$2\,115\,000

Source: domain.com.au

Which display conveys the information more effectively? Explain your answer.

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Outcomes

MS11-2

represents information in symbolic, graphical and tabular form

MS11-7

develops and carries out simple statistical processes to answer questions posed

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