Tables Charts & Graphs

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Relative Frequency

Reading Pie Charts

Tables Charts & Tables Charts & GraphsGraphs

Constructing Pie Charts

Cumulative Frequency Tables

Dot Plots

Cumulative Frequency Graphs

Five Figure Summary

Box Plots

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Starter QuestionsStarter Questions

31. Factorise 3x - 9

2. A car depreciates at 15% each year.

How much is it worth af ter 3 years if it cost

£ 12 000 initially.

3. What f raction is 80 out of a 100.

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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.

Relative Frequency

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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

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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

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Now try Exercise 1Ch10 (page 138)


Relative Frequency

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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

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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.

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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

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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

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Reading Pie Charts

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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.

A

B

C

8cm53o

70o

4cm

2cm3cm29o

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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.

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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

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Total 300

Rugby

Drawing Pie Charts


Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30


3009 ox


300

01 ox


3005 ox


3007 ox


3003 ox

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Total 300

Drawing Pie Charts


Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Rugby


3009 ox


300

01 ox


3005 ox


3007 ox


3003 ox

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Total 300

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30Footbal

l

Drawing Pie Charts


Rugby


3009 ox


300

01 ox


3005 ox


3007 ox


3003 ox

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Total 300

Drawing Pie Charts


Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Rug

b

y Footbal

l


3009 ox


300

01 ox


3005 ox


3007 ox


3003 ox

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Total 300

Cricket

Drawing Pie Charts


Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Rug

b

y Footbal

l


3009 ox


300

01 ox


3005 ox


3007 ox


3003 ox

20 Apr 2023

Total 300

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Drawing Pie Charts


Rug

by

Football

Cricke

t


3009 ox


300

01 ox


3005 ox


3007 ox


3003 ox

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Total 300

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30Ice Hockey

Squash

Drawing Pie Charts


Rug

by

Football

Cricke

t


3009 ox


300

01 ox


3005 ox


3007 ox


3003 ox

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Total 300

Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

90o108o

54o72o

36o

Drawing Pie Charts


RugbyFo

otba

l

l

Cricket Ice Hockey

Squash


3009 ox


300

01 ox


3005 ox


3007 ox


3003 ox

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Total

Drawing Pie Charts


Rugby

Football

Cricket

Ice Hockey

75

90

45

60

Favourite Sport

Squash 30

Worksheet Constructing a Pie Chart

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Constructing Pie Constructing Pie ChartsCharts

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11 28

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

and 10cm in diameter.

x x 21. Factorise

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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

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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


7

6 8

4

25

29

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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

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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.Waist Sizes Frequency

28” 7

30” 12

32” 23

34” 14

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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 FrequencyCumulative FrequencyGraphsGraphs

How to draw a How to draw a cumulative cumulative

frequency graphfrequency graph

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

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 FrequencyFrequency

GraphsGraphs

Sometimes called an S – curve

graph

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Cumulative Cumulative FrequencyFrequency

GraphsGraphs

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21. Factorise 5m - 45

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

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

10cm

90o

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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 Plot

Dot PlotDot Plot

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

Dot Plot

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.

Dot PlotCommon 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.

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Now try Ex. 6 (page 147)

Dot PlotDot Plot

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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.

33o

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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.

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

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

figures.


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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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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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 =

H =

Q1 =

102

6.5 85




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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 =

H =

Q1 =

102

6 8.54.5




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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.

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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.

Box Plot Box Plot

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

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

Semi Inter- Quartile Range = 3½ ÷ 2 = 1¾

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.

Semi Inter- Quartile Range = 6 ÷ 2 = 3

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.

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.

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

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

L

Lowest value =

137

137 186

Highest value =

186

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)

Box Plot Box Plot

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