Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie...

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Tables Charts & Tables Charts & Graphs Graphs 13 Jun 2022 13 Jun 2022 Created by Mr. Lafferty Maths Dept. Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts www.mathsrevision.com Constructing Pie Charts Cumulative Frequency Tables Dot Plots Cumulative Frequency Graphs Five Figure Summary Box Plots S5 Int2

Transcript of Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie...

Page 1: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Tables Charts & Tables Charts & GraphsGraphs

10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Relative Frequency

Reading Pie Charts

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Constructing Pie Charts

Cumulative Frequency Tables

Dot Plots

Cumulative Frequency Graphs

Five Figure Summary

Box Plots

S5 Int2

Page 2: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Starter Starter QuestionsQuestions

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S5 Int2

1 Factorize 3x3 – 9

2 A car depreciates at 15% per year. How much is it worth after 3 years, if it cost £12000 initially?

3 Write 85% as a common fraction in its simplest form.

Page 3: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Know the term relative Know the term relative frequency.frequency.

1. To understand the term relative frequency.

2.2. Calculate relative Calculate relative frequency from data frequency from data given.given.

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Relative FrequencyS5 Int2

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Relative FrequencyHow often an event happens compared

to the total number of events.

CountryCountry FrequencyFrequency Relative FrequencyRelative Frequency

FranceFrance 180180

ItalyItaly 9090

SpainSpain 9090

TotalTotal

Example : Wine sold in a shop over one week

Relative Frequency

180 ÷ 360 = 180 ÷ 360 =

90 ÷ 360 = 90 ÷ 360 =

90 ÷ 360 = 90 ÷ 360 =

360 360

0.25 0.25

0.25 0.25

0.5 0.5

1 1

Relative Frequency

always added up to

1

S5 Int2

Page 5: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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Relative Frequency How often an event happens compared to the total number of

events.

BoyBoyss

GirlsGirls TotalTotal

FrequencyFrequency 300300 200200

Relative Relative FrequencyFrequency

Example Calculate the relative frequency for boys and girlsborn in the Royal Infirmary hospital in December 2007.

Relative Frequency

500

0.6 0.4 1

Relative Frequency adds up to 1

S5 Int2

Page 6: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Question 1 Page Question 1 Page 138138

Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

This question gives a breakdown of 5 hours on watching sport on TV. The time is recorded to the nearest 5 minutes.

First, we create a table of values and work out the frequencies.

SPORT FREQUENCY (M)

REL. FREQCY

Football 120

Golf 60

Swimming 45

Athletics 30

Equestrian 15

Others 30

TOTAL

Tables Charts & Tables Charts & GraphsGraphs

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S5 Int2

Page 7: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Tables Charts & Tables Charts & GraphsGraphs

10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

We add the frequencies to get a total

SPORT FREQUENCY (M)

REL. FREQCY

Football 120

Golf 60

Swimming 45

Athletics 30

Equestrian 15

Others 30

TOTAL

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S5 Int2

300

Page 8: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

SPORT FREQUENCY (M)

REL. FREQCY

Football 120 120 ÷ 300 = 0.4

Golf 60 60 ÷ 300 = 0.2

Swimming 45 45 ÷ 300 = 0.15

Athletics 30 30 ÷ 300 = 0.1

Equestrian 15 15 ÷ 300 = 0.05

Others 30

TOTAL 300

SPORT FREQUENCY (M)

REL. FREQCY

Football 120

Golf 60

Swimming 45

Athletics 30

Equestrian 15

Others 30

TOTAL 30010 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Then we work out the fraction of time each sport takes

SPORT FREQUENCY (M)

REL. FREQCY

Football 120 120 ÷ 300 = 0.4

Golf 60

Swimming 45

Athletics 30

Equestrian 15

Others 30

TOTAL 300

SPORT FREQUENCY (M)

REL. FREQCY

Football 120 120 ÷ 300 = 0.4

Golf 60 60 ÷ 300 = 0.2

Swimming 45

Athletics 30

Equestrian 15

Others 30

TOTAL 300

SPORT FREQUENCY (M)

REL. FREQCY

Football 120 120 ÷ 300 = 0.4

Golf 60 60 ÷ 300 = 0.2

Swimming 45 45 ÷ 300 = 0.15

Athletics 30

Equestrian 15

Others 30

TOTAL 300

SPORT FREQUENCY (M)

REL. FREQCY

Football 120 120 ÷ 300 = 0.4

Golf 60 60 ÷ 300 = 0.2

Swimming 45 45 ÷ 300 = 0.15

Athletics 30 30 ÷ 300 = 0.1

Equestrian 15

Others 30

TOTAL 300

SPORT FREQUENCY (M)

REL. FREQCY

Football 120 120 ÷ 300 = 0.4

Golf 60 60 ÷ 300 = 0.2

Swimming 45 45 ÷ 300 = 0.15

Athletics 30 30 ÷ 300 = 0.1

Equestrian 15 15 ÷ 300 = 0.05

Others 30 30 ÷ 300 = 0.1

TOTAL 300

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S5 Int2

Page 9: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 202310 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept

Now try Exercise 1Ch10 (page 138)

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Relative FrequencyS5 Int2

Page 10: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Starter QuestionsStarter Questions

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2

1. Multiply out the brackets and simplif y

2(x - 5) - 3(7 - x)

2. Find the gradient and the y - intercept

1 f or the line with equation y = - 9x +

2

3. Factorise x - 64

S5 Int2

Page 11: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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Pie ChartsPie ChartsReading Pie Charts

1. To interpret information from Pie Charts.

1.1. Find the relative frequency Find the relative frequency for an angle with in a Pie for an angle with in a Pie Chart.Chart.

2.2. Use relative frequency to Use relative frequency to interpret Pie Chart interpret Pie Chart information.information.

S5 Int2

Page 12: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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Pie charts can be thought of as circle graphs.

Reading Pie Charts

1. Work out relative frequency of each angle.

2. Then multiply by the total amount that the circle represents.

Two step process

Page 13: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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A drinks machine dispenses 500 drinks on a Monday. The information is displayed in the pie chart. Use the information to find the number of each drink sold.

Tea72o

36o

Milk

Squash144o

108o

Coffee

Pie Charts

Milk

Squash

72 360 500 o o

108 360 500 o o

36 360 500 o o

144 360 500 o o

Use the two step process

Coffee

Tea 100

150

50

200

Page 14: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 202310 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept

Now try Exercise 2Ch10 (page 140)

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Reading Pie ChartsS5 Int2

Page 15: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Starter QuestionsStarter Questions

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1. Find the area of the triangle.

2. Write down the two conditions

f or using the cosine rule.

3. Find the length of AC.

S5 Int2

A

B

C

8cm53o

70o

4cm

2cm3cm29o

Page 16: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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Pie ChartsPie ChartsConstructing Pie Charts

1. To construct an accurate Pie-Chart from a given table using fractions of 360o.

1.1. Find fractions of 360Find fractions of 360oo. .

2.2. Use these fractions to Use these fractions to construct a Pie Chart given construct a Pie Chart given in a table. in a table.

S5 Int2

Page 17: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 2023Created by Mr. Lafferty Maths

Dept.

75 ÷ 300 × 360 = 90°

Relative Frequency

90 ÷ 300 × 360 = 108°

45 ÷ 300 × 360 = 54°

60 ÷ 300 × 360 = 72°

30 ÷ 300 × 360 = 36°

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Total 300

Page 18: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 2023 Created by Mr. Lafferty Maths Dept.

Total 300

75Rugby angle = 360 0

3009 ox

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

90Football angle = 360 8

300

01 ox

45Cricket angle = 360 4

3005 ox

60Ice Hockey angle = 360 2

3007 ox

30Squash angle = 360 6

3003 ox

Page 19: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 2023 Created by Mr. Lafferty Maths Dept.

Total 300

Rugby

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

75Rugby angle = 360 0

3009 ox

90Football angle = 360 8

300

01 ox

45Cricket angle = 360 4

3005 ox

60Ice Hockey angle = 360 2

3007 ox

30Squash angle = 360 6

3003 ox

Page 20: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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Total 300

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Rugby

75Rugby angle = 360 0

3009 ox

90Football angle = 360 8

300

01 ox

45Cricket angle = 360 4

3005 ox

60Ice Hockey angle = 360 2

3007 ox

30Squash angle = 360 6

3003 ox

Page 21: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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Dept.

Total 300

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30Footbal

l

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

Rugby

75Rugby angle = 360 0

3009 ox

90Football angle = 360 8

300

01 ox

45Cricket angle = 360 4

3005 ox

60Ice Hockey angle = 360 2

3007 ox

30Squash angle = 360 6

3003 ox

Page 22: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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Dept.

Total 300

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Rug

b

y Footbal

l

75Rugby angle = 360 0

3009 ox

90Football angle = 360 8

300

01 ox

45Cricket angle = 360 4

3005 ox

60Ice Hockey angle = 360 2

3007 ox

30Squash angle = 360 6

3003 ox

Page 23: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 2023 Created by Mr. Lafferty Maths Dept.

Total 300

Cricket

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Rug

b

y Footbal

l

75Rugby angle = 360 0

3009 ox

90Football angle = 360 8

300

01 ox

45Cricket angle = 360 4

3005 ox

60Ice Hockey angle = 360 2

3007 ox

30Squash angle = 360 6

3003 ox

Page 24: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 2023 Created by Mr. Lafferty Maths Dept.

Total 300

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

Rug

by

Football

Cricke

t

75Rugby angle = 360 0

3009 ox

90Football angle = 360 8

300

01 ox

45Cricket angle = 360 4

3005 ox

60Ice Hockey angle = 360 2

3007 ox

30Squash angle = 360 6

3003 ox

Page 25: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 2023 Created by Mr. Lafferty Maths Dept.

Total 300

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30Ice Hockey

Squash

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

Rug

by

Football

Cricke

t

75Rugby angle = 360 0

3009 ox

90Football angle = 360 8

300

01 ox

45Cricket angle = 360 4

3005 ox

60Ice Hockey angle = 360 2

3007 ox

30Squash angle = 360 6

3003 ox

Page 26: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 2023 Created by Mr. Lafferty Maths Dept.

Total 300

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

90o108o

54o72o

36o

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

RugbyFo

otba

l

l

Cricket Ice Hockey

Squash

75Rugby angle = 360 0

3009 ox

90Football angle = 360 8

300

01 ox

45Cricket angle = 360 4

3005 ox

60Ice Hockey angle = 360 2

3007 ox

30Squash angle = 360 6

3003 ox

Page 27: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 2023 Created by Mr. Lafferty Maths Dept.

Total

Drawing Pie Charts

In a survey, people were asked to indicate which one of five sports they liked best. The information is given in the table. Display the information in a pie chart.

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Worksheet Constructing a Pie Chart

Page 28: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Now try Exercise 3Ch10 (page 141)

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Constructing Pie Constructing Pie ChartsCharts

S5 Int2

Page 29: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Starter QuestionsStarter Questions

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11 28

2. Find the volume of a cone 15cm in height

and 10cm in diameter.

x x 21. Factorise

S5 Int2

Page 30: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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1.1. Add a third cumulative Add a third cumulative column to a frequency column to a frequency table.table.

1. To explain how to construct a cumulative Frequency Table.

Cumulative Frequency Cumulative Frequency TablesTables

S5 Int2

Page 31: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

You have 1 minute to come up with a question you can easily answer from the table.

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DayDay Freq.Freq.

(f)(f)

Example : This table shows the numberof cars sold by a motor dealership eachday over a seven day period.

2

1

5

6

3

1

2

3

4

5

A third column is added to keep a running total. This makes it easier to get the total number of items.

2

6

17

12

5

Cum. Freq.Cum. Freq.Total so farTotal so far

Cumulative Frequency Cumulative Frequency TablesTables

7

6 8

4

25

29

S5 Int2

Page 32: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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Cumulative Frequency Cumulative Frequency TablesTables

S5 Int2

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6

Num

ber

of S

tude

nts

Shoe Size

Construct a cumulative frequency table for this data

Frequency

C. Freq.

Total

1

234

56

Shoe Size14

51424

15

10

242630

30

1 minute to come up with

a question

Page 33: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Now try Exercise 4Ch10 (page 143)

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Cumulative Frequency Cumulative Frequency TablesTables

S5 Int2

Page 34: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Starter QuestionsStarter Questions

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10 2 - 5

2. Solve the simultaneous equations

x y and x y

1. Construct a cumulative frequency table

For the data below.

S5 Int2

Waist Sizes Frequency

28” 7

30” 12

32” 23

34” 14

Page 35: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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1.1. Be able to construct a Be able to construct a cumulative frequency cumulative frequency graph.graph.

1. To show how to construct a cumulative frequency graph from cumulative frequency table.

Cumulative Frequency Cumulative Frequency TablesTables

S5 Int2

Page 36: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Cumulative Cumulative Frequency GraphsFrequency Graphs

How to draw a How to draw a cumulative cumulative

frequency graphfrequency graph

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Page 37: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Km travelled on 1 gallon (mpg)

Frequency

Cumulative

Frequency

20 3 3

25 8 11

30 19 30

35 23 53

40 16 69

45 7 76

50 4 80

How to construct aCumulative Frequency Graph

Plot

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Page 38: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60

Cum

ulat

ive

Fre

quen

cy

Km travelled on 1 gallon (mpg)

Write down a question you

could ask about this

graph.

Cumulative Cumulative Frequency GraphsFrequency Graphs

Sometimes called an S – curve

graph

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Page 39: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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Now try Exercise 5Ch10 (page 145)

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Cumulative Cumulative Frequency GraphsFrequency Graphs

Page 40: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Starter QuestionsStarter Questions

10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

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2. Find the area of the shaded part of the circle.

3. Explain the meaning of the tangent to the circle.

S5 Int2

10cm

90o

Page 41: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

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1.1. Be able to construct a dot Be able to construct a dot and identify the key and identify the key features of various plots.features of various plots.

1. To show how to construct a dot plot and identify key feature..

Dot PlotDot PlotS5 Int2

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Dot PlotDot Plot

Dot plots are a very simple yet useful way of getting a feel for data using the number

line.

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Dot Plotw

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S5 Int2

Example : A group of students measure their pulse rates when resting.

The rates are 66, 69, 62, 58, 74, 56, 67, 72, 61, 62, 59

50 60 70 80

Write down as many key points that you

can deduce from the plot.

1. Lowest value is 56 BPM.2. Highest value is 74 BPM.3. Mode is 62.4. Median is also 62.5. Distribution is fairly flat.

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Dot Plotw

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S5 Int2Common expressions for various dot plots.

Symmetrical distribution Widely spread out distribution

Uniform distribution Tightly clustered distribution

Skewed to the right distribution Skewed to the left distribution

By looking at the shape of the distribution try and

describe the 6 types we have.

Page 45: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Now try Exercise 6Ch10 (page 147)

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Dot PlotDot Plot

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Starter QuestionsStarter Questions

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2

1. I f lines have the same gradient

What is special about them.

2. Factorise x +8x +15

3. Find the missing angles.

S5 Int2

33o

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.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Understand the termsUnderstand the terms

L , H, QL , H, Q11, Q, Q22 and Q and Q33..

1. To explain the meaning and show how to workout the five summary information for a set of data.

S5 Int2

Five Figure Five Figure SummarySummary

2.2. Be able to work Be able to work

L , H, QL , H, Q11, Q, Q22 and Q and Q33

For a set of dataFor a set of data

Page 48: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

When a set of numbers are put in ORDER, it can be summarised by quoting five

figures.

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Five Figure Five Figure SummarySummary

1. The highest number (H)

2. The lowest number (L)

3. The median, the number that halves the list (Q2)

4. The upper quartile, the median of the upper half (Q3)

5. The lower quartile, the median of the lower half (Q1)

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Five Figure SummaryFive Figure Summary

Example Find the five figure summary for the data.2, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10

L =

Q3 =

2 4 5 5 6 7 7 7 8 9 10

Q2 = Median (middle value)

Q2 =

H =

Q1 =

102

7 85

The 11 numbers are already in order !

Q3 = upper middle value

Q1 = lower middle value

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S5 Int2

Five Figure Five Figure SummarySummary

Example Find the five figure summary for the data.2, 4, 5, 5, 6, 7, 7, 8, 9, 10

L =

Q3 =

2 4 5 5 6 7 7 8 9 10

Q2 = Median (middle value)

Q2 =

H =

Q1 =

102

6.5 85

The 10 numbers are already in order !

Q3 = upper middle value

Q1 = lower middle value

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S5 Int2

Five Figure Five Figure SummarySummary

Example Find the five figure summary for the data.2, 4, 5, 5, 6, 7, 8, 9, 10

L =

Q3 =

2 4 5 5 6 7 8 9 10

Q2 = Median (middle value)

Q2 =

H =

Q1 =

102

6 8.54.5

The 9 numbers are already in order !

Q3 = upper middle value

Q1 = lower middle value

Page 52: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Now try Exercise 7Ch10 (page 150)

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Five Figure Five Figure SummarySummary

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Starter QuestionsStarter Questions

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.com 1. Write the five figure summary for the data below.

3, 1, 5, 5, 8, 2, 4, 6

2. The population of Glasgow was 1.2 Million.

I t increased by 5% each year for 4 years.

What is the population after the 4 years.

S5 Int2

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.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Be able to construct a box Be able to construct a box plot using the five figure plot using the five figure summary data.summary data.

1. To show how to construct a box plot using the five figure summary.

S5 Int2

Box Plot Box Plot

Page 55: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Two middle values so take the mean.

Averages (The Median)

The median is the middle value of a set of data once the data has been ordered.

Example 1. Robert hit 12 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives.

85, 125, 130, 65, 100, 70, 75, 50, 140, 135, 95, 70

Median drive = 90 yards

50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 135, 140

Ordered data

Page 56: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Finding the median, quartiles and inter-quartile range.

12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10

4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12

Order the data

Inter- Quartile Range = 9 - 5½ = 3½

Example 1: Find the median and quartiles for the data below.

Lower Quartile = 5½

Q1

Upper Quartile = 9

Q3

Median = 8

Q2

Page 57: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Upper Quartile = 10

Q3

Lower Quartile = 4

Q1

Median = 8

Q2

3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15,

Finding the median, quartiles and inter-quartile range.

6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10

Order the data

Inter- Quartile Range = 10 - 4 = 6

Example 2: Find the median and quartiles for the data below.

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4 5 6 7 8 9 10 11 12

MedianLower

QuartileUpper

QuartileLowest Value

Highest Value

BoxWhiskerWhisker

130 140 150 160 170 180 190

Boys

Girlscm

Box and Whisker Diagrams.

Box plots are useful for comparing two or more sets of data like that shown below for heights of boys and girls in a class.

Anatomy of a Box and Whisker Diagram.

Page 59: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Lower Quartile = 5½

Q1

Upper Quartile = 9

Q3

Median = 8

Q2

4 5 6 7 8 9 10 11 12

4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12

Example 1: Draw a Box plot for the data below

Drawing a Box Plot.

Page 60: Tables Charts & Graphs 3-Jun-14Created by Mr. Lafferty Maths Dept. Relative Frequency Reading Pie Charts  Constructing Pie Charts.

Upper Quartile = 10

Q3

Lower Quartile = 4

Q1

Median = 8

Q2

3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15,

Example 2: Draw a Box plot for the data below

Drawing a Box Plot.

3 4 5 6 7 8 9 10 11 12 13 14 15

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Upper Quartile = 180

Q3

Lower Quartile = 158

Q1

Median = 171

Q2

Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data.

Drawing a Box Plot.

137, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186

130 140 150 160 170 180 190cm

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2. The boys are taller on average.

Question: Gemma recorded the heights in cm of girls in the same class and constructed a box plot from the data. The box plots for both boys and girls are shown below. Use the box plots to choose some correct statements comparing heights of boys and girls in the class. Justify your answers.

Drawing a Box Plot.

130 140 150 160 170 180 190

Boys

Girls

cm

1. The girls are taller on average.

3. The girls show less variability in height.

4. The boys show less variability in height.

5. The smallest person is a girl

6. The tallest person is a boy

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Now try Ex 8 & 9Ch10 (page 152)

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Box Plot Box Plot