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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
Starter Starter QuestionsQuestions
10 Apr 202310 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Deptww
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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.
Tables Charts & Tables Charts & GraphsGraphs
10 Apr 202310 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Dept
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
Tables Charts & Tables Charts & GraphsGraphs
10 Apr 202310 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Deptww
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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
Tables Charts & Tables Charts & GraphsGraphs
10 Apr 202310 Apr 2023 Created by Mr Lafferty Maths DeptCreated by Mr Lafferty Maths Deptww
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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
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
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
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
Tables Charts & Tables Charts & GraphsGraphs
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S5 Int2
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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Tables Charts & Tables Charts & GraphsGraphs
Relative FrequencyS5 Int2
Starter QuestionsStarter Questions
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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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
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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
10 Apr 2023 Created by Mr. Lafferty 12
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
10 Apr 2023 Created by Mr. Lafferty 13
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
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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Tables Charts & Tables Charts & GraphsGraphs
Reading Pie ChartsS5 Int2
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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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
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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
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
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
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
10 Apr 2023 Created by Mr. Lafferty Maths 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
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
10 Apr 2023Created by Mr. Lafferty Maths
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
10 Apr 2023Created by Mr. Lafferty Maths
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
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
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
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
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
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
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
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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11 28
2. Find the volume of a cone 15cm in height
and 10cm in diameter.
x x 21. Factorise
S5 Int2
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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
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
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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
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
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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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
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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
Cumulative Cumulative Frequency GraphsFrequency Graphs
How to draw a How to draw a cumulative cumulative
frequency graphfrequency graph
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S5 Int2
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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S5 Int2
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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S5 Int2
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 5Ch10 (page 145)
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S5 Int2
Cumulative Cumulative Frequency GraphsFrequency Graphs
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
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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
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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S5 Int2
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.
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.
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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S5 Int2
Dot PlotDot Plot
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
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
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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.
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
When a set of numbers are put in ORDER, it can be summarised by quoting five
figures.
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S5 Int2
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)
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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S5 Int2
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
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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
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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S5 Int2
Five Figure Five Figure SummarySummary
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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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
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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.
S5 Int2
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
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.
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
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
10 Apr 202310 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Ex 8 & 9Ch10 (page 152)
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S5 Int2
Box Plot Box Plot