20 Apr 202320 Apr 2023
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
20 Apr 202320 Apr 2023
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.
20 Apr 202320 Apr 2023
Tables Charts & Tables Charts & GraphsGraphs
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
20 Apr 202320 Apr 2023
Tables Charts & Tables Charts & GraphsGraphs
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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Tables Charts & Tables Charts & GraphsGraphs
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
20 Apr 202320 Apr 2023
Now try Exercise 1Ch10 (page 138)
Tables Charts & Tables Charts & GraphsGraphs
Relative Frequency
20 Apr 202320 Apr 2023
Starter QuestionsStarter Questions
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
20 Apr 202320 Apr 2023
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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
20 Apr 2023 10
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
20 Apr 202320 Apr 2023
Now try Exercise 2Ch10 (page 140)
Tables Charts & Tables Charts & GraphsGraphs
Reading Pie Charts
20 Apr 202320 Apr 2023
Starter QuestionsStarter Questions
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
20 Apr 202320 Apr 2023
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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.
20 Apr 2023
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
20 Apr 2023
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
20 Apr 2023
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
20 Apr 2023
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
20 Apr 2023
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
20 Apr 2023
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
20 Apr 2023
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
20 Apr 2023
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
20 Apr 2023
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
20 Apr 2023
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
20 Apr 202320 Apr 2023
Now try Exercise 3Ch10 (page 141)
Constructing Pie Constructing Pie ChartsCharts
20 Apr 202320 Apr 2023
Starter QuestionsStarter Questions
11 28
2. Find the volume of a cone 15cm in height
and 10cm in diameter.
x x 21. Factorise
20 Apr 202320 Apr 2023
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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
Cumulative Frequency Cumulative Frequency TablesTables
7
6 8
4
25
29
20 Apr 202320 Apr 2023
Cumulative Frequency Cumulative Frequency TablesTables
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
20 Apr 202320 Apr 2023
Now try Exercise 4Ch10 (page 143)
Cumulative Frequency Cumulative Frequency TablesTables
20 Apr 202320 Apr 2023
Starter QuestionsStarter Questions
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
20 Apr 202320 Apr 2023
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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
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
20 Apr 202320 Apr 2023
Now try Exercise 5Ch10 (page 145)
Cumulative Cumulative FrequencyFrequency
GraphsGraphs
20 Apr 202320 Apr 2023
Starter QuestionsStarter Questions
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
20 Apr 202320 Apr 2023
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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.
20 Apr 202320 Apr 2023
Now try Ex. 6 (page 147)
Dot PlotDot Plot
20 Apr 202320 Apr 2023
Starter QuestionsStarter Questions
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
20 Apr 202320 Apr 2023
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.
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.
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 Five Figure SummarySummary
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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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
20 Apr 202320 Apr 2023
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
20 Apr 202320 Apr 2023
Now try Exercise 7Ch10 (page 150)
Five Figure Five Figure SummarySummary
20 Apr 202320 Apr 2023
Starter QuestionsStarter Questions
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.
20 Apr 202320 Apr 2023
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.
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
20 Apr 202320 Apr 2023
Now try Ex 8 & 9Ch10 (page 152)
Box Plot Box Plot