21. [Statistics / Probability] - Maths Mate NZ · Each Each= 2 hours = 1 hour Each= 2 medals = 1...

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21. [Statistics / Probability]

Skill 21.Skill 21.1 Interpreting stacked bar graphs without a scale.Interpreting stacked bar graphs without a scale.

Compare the length of each shaded bar.

Q. Which group of Australians represent the smallest proportion of our over 18 population?

A. Self funded retirees

b) Which coloured medal did Canadians win second most at the 2010 Vancouver Winter Olympics?

a) Australian and English cricketers have played for the Ashes since 1876. Which country has had the most wins?

d) Which of the ancient Chinese dynasties reigned for the least amount of time?

c) What is the main metal in British Pewter?

f) Which of the types of adult body tissue shown has the lowest percentage of water?

e) Which category had the most additions to the Hollywood Walk of Fame in 2012?

DrawAustraliaEngland

Ashes Series

AUSTRALIAN Population over 18 years

Self fundedretirees

Otherpensioners

Agedpensioners

Employees Students& other

Self funded retireesis the shortest length bar.

GOLDSILVERBRONZE

WINTER OLYMPIC MEDALS(Vancouver 2010)

Length of ancient Chinese Dynasties

Three sovereigns and five emperors

ZhouShangXia

Typical Composition of British Pewter

CopperAntimonyTin

RadioMusical/Recording

Television MotionPictures

JENNIFER ANNISTONJENNIFER ANNISTON

Hollywood Walk of Fame - 2012 additions

FatBloodMuscle Bone

Adult body tissue - percentage of water by weight

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Skill 21.Skill 21.2 Interpreting stacked bar graphs with a scale.Interpreting stacked bar graphs with a scale.

$

%

Q. What percentage of a typical 50 cent piece is copper?

A. 75%

b) How many irons are there in this set of golf clubs?

d) What percentage of 12 year olds have intermediate photographic skills?

a) Which chemical element makes up the largest proportion of the Earth’s mass?

f) How much is spent on lollies and video games each week?

e) Which sector employs 15% of New Zealanders?

c) How many forwards in a rugby union team?

The copper section of the bar is shaded white.It runs from 25% to 100%.100 − 25 = 75

Iron Oxygen OtherMagnesium

0 10 20 30 40 50 60 70 80 90 100%

Silicon

Chemical composition of the Earth (by mass)

Video Games

Lollies

CD’s

Savings

Pocket Money(Spending each week)

$0

$3

$6

$9

$12

$15

Dol

lars

0 25 50 75 100%

Typical composition of a 50¢ piece

Nickel Copper

Driver Wood Iron Putter

Set of Golf Clubs

Wedge

0 2 4 6 8 10 12 14

New ZealandEmploymentSectors

0

20

40

60

80

100

rural

manufacturing

service

Per

cent

age

Beginner Intermediate Advanced

Photographic skill of 12 year olds

0 20 40 60 80 100%

Backs Forwards

Rugby Union Team

0 3 6 9 12 15

Number of players

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Skill 21.Skill 21.3 Interpreting pictographs without a scale.Interpreting pictographs without a scale.

The silver category has 4 complete medals and half a medal.

Q. How many silver medals did Italy win at the London 2012 Olympics?

A. 2 + 2 + 2 + 2 + 1 = 9

c) Which city is a 5 hour drive from Berlin?

b) How many par 4 holes on the Augusta National golf course?

a) How many premolars does a human have?

d) What is the population of Birmingham?

........................................................................................

• Add the value of each symbol in the category.

Berlin - Paris

Berlin - Warsaw

Berlin - Amsterdam

Drive Time

= 2 hoursEach Each = 1 hour

= 2 medalsEach Each = 1 medal

London 2012 Olympics - Italy

Gold

Bronze

Silver

= 2 medalsEach Each = 1 medal

London 2012 Olympics - Italy

Gold

Bronze

Silver

Human Teeth

= 4 teetheach

Incisors Canines Premolars Molars

2 2 2 12

= 2 holesEach

par 3

par 4

par 5

Augusta National

LONDON

Leeds

Manchester

Nottingham

Birmingham

ENGLAND

= 1,000,000 people

= 100,000 people

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Skill 21.Skill 21.4 Interpreting pictographs with a scale (1).Interpreting pictographs with a scale (1).

Each interval on the scale equals one instrument.There are 18 woodwind instruments.There are 12 brass instruments.18 − 12 = 6

a) Which space shuttle has spent closest to 1 year in space?

c) How many Brownlow medals in total have been won by Essendon and the Sydney Swans?

b) Which landmark is closest to 70 m in height?

d) In which year did Beyonce win her 9th grammy award?

Q. How many more woodwind than brass instruments are in the ABC Symphony Orchestra?

A. 6

0

1

2

3

4

5

6

Num

ber o

f Gra

mm

ys

201120102007 2008 20092006

Grammy Awards - Beyonce

20042002 2003 200520012000

0 5 10 15 20 25 30

Percussion

Brass

Woodwind

String

Inst

rum

ents

Instruments in the ABC Symphony Orchestra

0 5 10

12 18

15 20 25 30

Percussion

Brass

Woodwind

String

Inst

rum

ents

Instruments in the ABC. Symphony Orchestra

Number of Brownlows0 2 4 6 8 10 12 14

Essendon

WesternBulldogs

St Kilda

SydneySwansC

lub

AFL Brownlow medal winners1924 - 2012 (top 4 clubs)

0

50

100

Statueof

LibertyUSA

BigBenUK

LeaningTowerof PisaItaly

BrandenburgGate

Germany

Sydney Opera HouseAustralia

Hei

ght (

m) Famous Landmarks

0 50 100 150 200

*Days in space

Space Shu les - NASA

250 300 350 400

Atlan s

Endeavour

Discovery

Challenger

Columbia

*as of Feb 2011

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Skill 21.Skill 21.4 Interpreting pictographs with a scale (2).Interpreting pictographs with a scale (2).

e) How many cars per 100 people are there in Canada?

g) Name the cities with metro systems between 300 and 400 kilometres in length.

f) Pain is felt once a sound goes beyond 125 decibels. How many of these sounds would hurt your ears?

h) How many of the years shown had between 600 and 700 birds hitting high capacity aeroplanes.

i) Which Enid Blyton Series has 15 books? j) Which of these billionaires has a wealth of approximately 50 billion dollars?

Number of cars per 100 people0 20 40 60 80 100

Canada

New Zealand

Africa

U.S.A.

Europe

World ACCESS TO CARS

0 100SOUND LEVEL (decibels)

200

rocket launch

thunder clap

library

amplified rock music

hair dryer

normal conversation

NOISE

0 100 200 300 400 500kilometres

= 100 kmLONGEST METRO SYSTEMS

Tokyo

Moscow

Paris

New York

London

Famous fiveEnid Blyton’s series

St Clare’s

Noddy

Secret seven

Magic faraway tree

Malory towers

5 10 15 200

LawrenceEllison

BernardArnault

WarrenBuffet

BillGates

CarlosHelu

Wea

lth

($U

S bi

llion

s)

0

15

30

45

60

75BILLIONAIRES

0 100 200 300 400 500

number of bird strikes

Bird strikes on high capacity aeroplanes

600 700 800 900

2002

2003

2004

2005

2006

2007

2008

2009

2010

Year

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Skill 21.Skill 21.5 Interpreting tables.Interpreting tables.

km

First find the‘girls’ column.

Then check participation rates down the column. The highest is 24%.

Trace the 24% back along the row to its title, dancing.

Q. Which lessons are Australian girls most likely to choose?

A. Dancing

• Check what each row and column represents.

c) Which group, males or females, are twice as likely to play with the Wii as their primary console?

d) How far is it from Invercargill to Queenstown?

b) Which Imperial ship is closest in length to the Rebellion ship the Y-wing?

a) Which Australian state recorded the earthquake with the highest magnitude?

Console

Primary Console Players

Females

38%

Wii

X box 360

Males

41%

11%

80%

PS3 21%9%

27.05.2013

Date

25.05.2013

25.05.2013

22.05.2013

22.05.2013

Magnitude

2.4

1.7

4.9

2.5

2.6

NE of Koorda

NW of Koorda

W of Macquarie Island

S of Mundubbera

Franklin River

Location State

WA

WA

WA

QLD

WA

Earthquakes in Australia

Cultural lessons - Australian Children (5 - 14)

ClassMusical Instrument

Participation Rate (%)Girls

13

Boys

22

Singing 3 7

Dancing 24

Drama 3 6

2

Cultural lessons - Australian Children (5 - 14)

ClassMusical Instrument

Participation Rate (%)Girls

13

Boys

22

Singing 3 7

Dancing 24

Drama 3 6

2

Rebellion Ships

X-wing

Length(m)

Length(m)

12.5

Imperial Ships

Twin-Ion Engine Starfighters (TIE)

6.3

Y-wing 16 Imperial Shuttle 20B-wing 16.9 AT - AT 14Blockade Runner 150 Imperial

Star Destroyer1600

Mon CalamariCruiser

1200 Death Star 120 000

Road distances between some major cities, given in kilometres.

Dunedin

Franz Josef

Invercragill

Milford Sound

Mt Cook

Queenstown

Westport

Chr

istc

hurc

h

Dun

edin

Fra

nz J

osef

Inve

rcra

gill

Milf

ord

Sou

nd

Mt C

ook

Que

enst

own

South Island New Zealand

360

408

578

764

418

487

333

567

217

402

331

283

695

581

686

500

408

280

280

445

187

861

558

307

996

266

664 688

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Skill 21.Skill 21.6 Interpreting bar graphs (1).Interpreting bar graphs (1).

kg

km/h

Check the scale along the base of the graph. The more visits to the doctor, the longer the bar.

The longest bar is beside‘Throat problems’.

Q. What was the most common reason for children to visit the doctor?

A. Throat problems

a) What speed can a koala reach? b) Which of the countries shown has the tallest woman?

d) What is the weight of a newborn giraffe? [Give your answer to the nearest ten.]

c) Name the planet with the greatest diameter.

Spee

d (k

m/h

)

0

10

20

30

40

50

60

70

CrocodileAnimal

KoalaGreyKangaroo

RedKangaroo

How fast?

Throatproblems

Chestinfection

Skinproblems

Vaccination

Checkup

Reas

on

0 100 200 300 400 500

Earproblems

Why children visit the doctor

Consultation rate (per 1000 children)

0 kg

20 kg

40 kg

60 kg

80 kg

100 kg

120 kg

GiraffeGorillaElephantClydesdale(horse)

PolarBear

Hippopotamus

Newborn weight

Wei

ght

(kilo

gram

s)

30 000

0

60 000

90 000

120 000

150 000

Neptune

UranusSaturn

Jupite

rMars

Venus

Mercury Planet

Dia

met

er (

km)

OUR SOLAR SYSTEM(Diameters of planets)

Earth

1.5

0

1.6

1.7Av

erag

e adu

lt he

ight (

m)

FranceChina Canada

Average height of females (selected countries)

BrazilAustraliaNew

Zealand

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Skill 21.Skill 21.6 Interpreting bar graphs (2).Interpreting bar graphs (2).

f) How many of baseball’s great hitters have made over 700 home runs?

e) How many more lighthouses are there in Queensland than Victoria?

j) Which continent is closest to 15 million square kilometres in area?

i) The underground railway system in which city has nearly the same number of stations as kilometres in its length?

h) Harry booked the 398th and last seat in the room. Which part of the Sydney Opera House was Harry in?

g) Who is closest to filling Shaquille O’Neals’ one shoe with two shoes?

Number of seats

Playhouse

Studio

Drama Theatre

Opera Theatre

Concert Hall

RoomSydney Opera House

0 500 1000 1500 2000 2500 3000SportsmanTigerWoods

ShaquilleO’Neal

LleytonHewitt

IanThorpe

MichaelJordan

Siz

e (U

SA

)

Fill these shoes!

DavidBeckham

0

5

10

15

20

25

0 100 200 300 400 500

0 100 200 300 400 500

number of stations

Tokyo

New York

Moscow

London

Paris

length of underground system (km)

0 100 200 300 400 500 600 700 800

Ty Cobb

Hank Aaron

Baseball’s Great Hitters

Home runs

Babe Ruth

Mickey Mantle

Willie Mays

Lou Gehrig

0

10

20

30

40

50

AfricaAntarcticaAsiaAmericaOceaniaEurope

Are

a (m

illio

n s

q. k

m) AREA OF CONTINENTS

0

10

20

30

40

Num

ber o

f lig

htho

uses

VICNSWQLDNTStates

Lighthouses in Australia

WASATas

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Skill 21.Skill 21.7 Interpreting multiple stacked bar graphs.Interpreting multiple stacked bar graphs.

Q. Which of these monkeys has the shortest average tail length?

A. Snow monkey

b) Which of the 3 countries shown has the largest percentage of under 15 year olds in their population structure?

c) Which country has the greatest number of public holidays?

a) In which round of the 2013 Australian Masters did Karrie Webb score the least pars?

d) Which expense is greater than the cost of food for both dog and cat owners?

Check the scale along the base of the graph. The shorter the tail length, the shorter the bar.

Check the key. The white bars represent the tail. The shortest white bar is beside the snow monkey.

0 30 60 90

Average Head/Body and Tail Lengthsof Selected Monkey Breeds

120 150Average length (cm)

Tail

Head/Body

Squirrel

Spider

Snow

Howler

Colobus

Monkey

0 10 20 30

Average Head/Body and Tail Lengthsof Selected Monkey Breeds

40 50 60Average length (inches)

Tail

Head/Body

Squirrel

Spider

Snow

Howler

Colobus

Monkey

0 20 40 60 80 100 %

Over 60 yr

Population structure

15 - 60Under 15

Japan

Australia

Kenya

0

20

40

60

80

100

Perc

enat

ge

(%)

vet

Type of cost

Annual costs for cat and dog owners

treats

grooming

kennel/cattery

food

cat dog

0

3

6

9

12

15

Round

Par

Birdie

Bogey

2013 Australian Ladies MastersResults - Karrie Webb

Num

ber

of h

oles 18

1 2 3

Annual Leave

Public HolidaysTIME OUT(Days Off Work)

0 5 10 15 20 25 30 35

Australia

New Zealand

Japan

USA

Days

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Skill 21.Skill 21.8 Recognising the relative likelihood of an event.Recognising the relative likelihood of an event.

a) Choose the best phrase (is likely to / is unlikely to / will not) to complete this statement:

“The moon

collide with the Earth tonight.”

h) Choose the best phrase (is certain to / is likely to / is unlikely to / will not) to complete this statement:

“Beethoven have

played the piano.”

g) Choose the best phrase (is certain to / is likely to / is unlikely to / will not) to complete this statement:

“A Russian

win a Commonwealth Games gold medal.”

f) Choose the best phrase (is certain to / is likely to / is unlikely to / will not) to complete this statement:

“The Southern Cross

be in the

Southern sky.”

e) Which alternative is closest in meaning to the expression “Fat chance”? A ) 50 - 50 chance B ) unlikely C ) certain

d) Which alternative is closest in meaning to the expression “It’s a toss up”? A ) 50 - 50 chance B ) unlikely C ) impossible

Consider each alternative.Par on a golf course is set so that ‘some’ people can achieve it.Par is neither certain, nor impossible.

Q. Which alternative is closest in meaning to the expression “Par for the course”? A ) certain B ) likely C ) impossible

A. B

b) Which alternative is closest in meaning to the expression “Find a needle in a haystack”? A ) occurs about half the time B ) not common C ) extremely rare

c) Which alternative is closest in meaning to the expression “Skating on thin ice”? A ) most likely to succeed B ) unlikely to succeed C ) certain to succeed

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Skill 21.Skill 21.9 Finding the number of objects to achieve a given outcome.Finding the number of objects to achieve a given outcome.

It is possible to pick these letters first:H, I, T, E, TThen it is possible to pick these letters:C, CThe next pick will either be an A or an Rand still the word CAR cannot be formed.Therefore all 9 letters must be picked to be certain that the word CAR is formed.

Q. A bag contains the letters A R C H I T E C T Letters are drawn at random. How many letters do you need to pick from the box to be certain you can make the word CAR?

A. 9

c) You have 10 light bulbs and 3 do not work. What is the smallest number of light bulbs you must check to be certain of having a good one?

g) A bag contains the letters M E A S U R E M E N T Letters are drawn at random. How many letters do you need to pick from the box to be certain you can make the word ME?

h) A bag contains the letters M I S S I S S I P P I Letters are drawn at random. How many letters do you need to pick from the box to be certain you can make the word SIP?

a) You have six 10-cent coins and ten 20-cent coins in your pocket. What is the smallest number of coins you need to take out of your pocket to be certain of having at least one of each coin?

b) In the game of Mahjong there are 16 wind tiles, 4 each of North, South, East and West. If the tiles are turned face down on the table, how many tiles do you need to select to be sure to choose at least one East wind?

d) There are 6 orange, 8 blue and 10 red flippers in the swimming bag. How many flippers must you take out of the bag, without looking, to be sure you have a pair of orange flippers?

e) There are six pairs of runners in the back of Mike’s closet. Because the closet is dark, how many individual runners must he take out of the closet to make sure he has a matching pair of runners?

f) A shop keeper has six green cricket pads, four red pads and two white pads in the store room. There is a power failure and he reaches into the room in the dark. How many pads must he take out to be certain of having at least two green cricket pads?

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Skill 21.Skill 21.1010 Describing the likelihood of an outcome.Describing the likelihood of an outcome.

Only 2 of the 14 marbles are white.Only 2 out of 14 draws will give a white marble.

It is not impossible but it is unlikely that with your first draw you will pick a white marble.There are 12 chances to draw a green marble.

Q. A bag contains 2 white marbles and 12 green marbles. What is the chance that the first marble drawn will be white? A ) impossible B ) unlikely C ) likely D ) certain

A. B

d) A bag contains 8 white marbles and 4 green marbles. What is the chance that the first marble drawn will be white? A ) impossible B ) unlikely C ) likely D ) certain

b) A bag contains 4 white marbles and 4 green marbles. What is the chance that the first marble drawn will be orange? A ) impossible B ) unlikely C ) likely D ) certain

a) In a lotto draw, balls numbered 1 to 50 are mixed together. A machine then randomly selects balls numbered 8, 14, 2, 26 and 42. Is the sixth number drawn: A ) more likely to be odd than even, B ) more likely to be even than odd or C ) just as likely to be odd as even?

c) In a lotto draw, balls numbered 1 to 50 are mixed together. A machine then randomly selects balls numbered 8, 14, 2, 21 and 17. Is the sixth number drawn: A ) more likely to be more than 25, B ) more likely to be less than 25 or C ) just as likely to be less than 25 as more than 25?

e) A pack contains 5 white, 9 purple, 6 green and 3 orange jelly beans. What is the chance that the first jelly bean taken will be purple? A ) impossible B ) unlikely C ) likely D ) certain

f) Amanda has six $1 coins and twelve $2 coins in her pocket. What is the chance that the first coin she takes out will be a $1 coin? A ) impossible B ) unlikely C ) likely D ) certain

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Skill 21.Skill 21.1111 Calculating the probability of a simple event (1).Calculating the probability of a simple event (1).

a) What is the probability of drawing a Queen from a standard deck of playing cards? [Give the answer as a fraction in its simplest form.]

Q. What is the probability of rolling a number greater than 2 with one roll of a die? [Give the answer as a fraction in its simplest form.]

A.

b) What is the probability of throwing a dart inside an 11-point area when you hit the dart board? [Give the answer as a fraction in its simplest form.]

c) Each of the letters in PROBABILITY is put into a bag. If a letter is randomly selected, what is the probability of choosing a consonant? [Give the answer as a fraction in its simplest form.]

• Find the number of favourable outcomes for the event.• Find the total number of possible outcomes.• Divide the number of favourable outcomes by the number of possible outcomes.

Event: rolling a number greater than 2Favourable outcomes (FO): 4 (rolling 3, 4, 5 or 6)Possible outcomes (PO): 6 (rolling 1, 2, 3, 4, 5, or 6)Probability: 4 out of 6

or

23

46

23

=÷ 2

÷ 2

÷ 4

÷ 4

452

113

FOPO

= = ÷ 3

÷ 3

312

FOPO

=

d) A money bag contains twenty 50-cent coins and sixty 10-cent coins. A coin is randomly selected. What is the probability of a 50-cent coin being selected? [Give the answer as a fraction in its simplest form.]

............................................................................................ ............................................................................................

FOPO

= FOPO

=

............................................................................................ ............................................................................................

Probability of an event = number of favourable outcomesnumber of possible outcomes

11

13

7 3

2

11 5

2 7

5

11

3

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Skill 21.Skill 21.1111 Calculating the probability of a simple event (2).Calculating the probability of a simple event (2).

e) A spinner is spun. What is the probability that it will stop on an even number? [Give the answer as a fraction.]

f) A spinner is spun. What is the probability that it will stop on an odd number? [Give the answer as a fraction.]

............................................................................................ ............................................................................................

FOPO

= FOPO

=

i) What is the probability of rolling a number less than 5 with one roll of a die? [Give the answer as a fraction.]

j) What is the probability of rolling an even number with one roll of a die? [Give the answer as a fraction.]

............................................................................................ ............................................................................................

FOPO

= FOPO

=

............................................................................................ ............................................................................................

FOPO

= FOPO

=

g) A box has 10 chocolate, 10 plain and 12 creamed biscuits. If a biscuit is randomly selected from the box, what is the probability of choosing a plain biscuit? [Give the answer as a fraction.]

h) A deck of cards has 5 navy, 5 yellow and 5 black cards. A card is randomly picked from the deck. What is the probability of a black card being picked? [Give the answer as a fraction.]

............................................................................................ ............................................................................................

FOPO

= FOPO

=

k) Ben and 11 other athletes are racing in the 800 m event. What is the probability that Ben will win one of 3 medals? [Give the answer as a fraction.]

l) Janet bought 20 raffle tickets. If there are 200 tickets altogether, what is the probability that one of her tickets will win? [Give the answer as a fraction.]

7

5

11

133

21

281

10

6

3

15

36

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Skill 21.Skill 21.1212 Interpreting pie charts.Interpreting pie charts.

%

Look for the smallest sector of the circle.South America is slightly smaller than Oceania.

Q. Which continent has the least number of countries?

A. South America

a) What percentage of children in the USA live with their mother only?

b) Which part of an insulated brick veneer home is responsible for one quarter of the heat loss in winter?

c) If you were one of the 65 000 000 households in the USA to have dogs as a pet, how many are you most likely to have?

d) Which age group accounts for closest to 20% of all facebook users?

• Consider each section of the pie chart as a sector of a circle (pie).

Households With Dogs

3 dogs

2 dogs

1 dog

Africa

Asia

Europe

Oceania

South America

North America

Number of Countries by Continent

mother only

father only

married couple

Child Population by Household USA

25%

Insulated Brick VeneerHeat Loss in Winter

Ventilation PointsWindowsWallsFloorCeiling & Roof

55-64 years

45-54 years

26-34 years

13-17 years

Facebook Users by age (years) 2011

18-25 years

35-44 years

25%

90° 180° 270° 360°

100%75%50%

PIE CHARTSEach piece of pie represents a percentage of the total.

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21. [Statistics / Probability] - Maths Mate NZ · Each Each= 2 hours = 1 hour Each= 2 medals = 1...

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Transcript of 21. [Statistics / Probability] - Maths Mate NZ · Each Each= 2 hours = 1 hour Each= 2 medals = 1...