Www.mathsrevision.com S3.3 Tables & Charts 11-Jun-14Created by Mr. [email protected]...

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S3.3

Tables & ChartsTables & Charts

Apr 10, 2023Apr 10, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com

Frequency Tables / Relative Frequency

Five Figure Summaries

Cumulative Frequency Table

Stem-leaf Diagrams

Back to Back Stem Leafs

Scatter Diagrams

Box Plots

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Starter QuestionsStarter Questions


Q1. Does 5x2 – 16x + 3 factorise to (5x - 1)(x – 3)

Q2. Change into £’s €75

exchange rate £1 € 1.5

Q3. Convert to scientific notation 0.0675

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10 Apr 202310 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty 33

Aims of the Lesson

1. Understand the term

Frequency Table and Relative Frequency .

2. Construct a Frequency/Relative Frequency Table.

3. Interpret information from Tables.

10 Apr 2023 4

Raw data can often appear untidy and difficult to understand. Organising such data into frequency tables can make it much easier to make sense of (interpret) the data.

Frequency tables

Data Tally Frequency

Sum of Tally is the Frequency

llll represents a tally of 5

10 Apr 2023 Created by Mr. Lafferty 5

Example 1. A tomato grower ideally wants his tomatoes to have diameters of 60mm, but a diameter ranging from 58mm to 62mm will be acceptable. Organise the diameters given below into a frequency table.

58

59

58

56

62

56

57

60

61

59

59

57

60

60

56

59

58

58

59

56

61

60

56

58

58

62

59

58

6061596257

5960566160

6258616260

5956586262

Frequency tables

Lowest number 56

Highest number 62


Diameter Tally Frequency

56

57

58

59

60

61

62

l

l

l

l

l

l

Frequency tables

58

60

58

56

59

59

57

60

61

59

59

57

60

60

56

59

58

58

59

56

61

60

57

58

58

62

59

58

6061596257

5960596159

6258615960

5960586062X X X X X X


Diameter Tally Frequency

56

57

58

59

60

61

62

Total

Frequency Tables

3

4

9

13

5

10

4

lll

llll

llll

llll

llll

llll

llll llll lll

llll

llll

58

60

58

56

59

59

57

60

61

59

59

57

60

60

56

59

58

58

59

56

61

60

57

58

58

62

59

58

6061596257

5960596159

6258615960

5960586062X X X X X X X X X X X X

X X X X X X X X X X X XX X X X X X X X X X X XX X X X X X X X X X X X

Relative Frequency

R48

3 ÷ 48 = 0.0625

4 ÷ 48 = 0.0833

9 ÷ 48 = 0.1875

13 ÷ 48 = 0.2708

10 ÷ 48 = 0.2083

5 ÷ 48 = 0.1042

4 ÷ 48 = 0.0833

Relative Frequency

always adds up to 1

Relative Frequency used with Pie charts

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10 Apr 202310 Apr 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com

Now try Ex 3.1Q2

Ch6 MIA (page 108)

Charts & TablesCharts & Tables

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

1. Find the mean, range and median for the set of data.

9, 1, 5, 5, 8, 2, 4, 6

Q2. Find the area for the shapes

Q3. Write in standard form 0.008654

(w - 2)

7

(x – 5)

(x – 3)

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Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Add a third column to a Add a third column to a frequency table to create a frequency table to create a Cumulative Frequency Cumulative Frequency Table.Table.

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

Cumulative Cumulative Frequency TablesFrequency Tables

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DayDay Freq.Freq.

(f)(f)

Example : This table shows the numberof eggs laid by a clutch of chickens 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

(Cumulative Frequency Table). 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

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

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Now try Ex 3.2Ch6 (page 109)


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Q1. Factorise

4x2 + 9x - 9

Q2. Multiply out

(a) a(ab – a) (b) -2a( b2 – a)

Q3. 3 7

5 15

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1. To construct a Stem-Leaf Graph / Dot Graph and answer questions based on it.

1. Construct and understand the Key-Points of a Stem-Leaf Graph / Dot Graphs.

Stem Leaf GraphsStem Leaf GraphsConstruction of Stem-Leaf

2. Answer questions based on the graph.

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Stem Leaf GraphsStem Leaf GraphsConstruction of Stem and Leaf

A Stem – Leaf graph is another way of displaying information :

This stem and leaf graph shows the ages of people waiting in a queue at a post office

2 4 6 8

3 0 1 3

4 4 4 5 6 7 9

5 0 3 4 9

6 1 4 5 6

stem leaves

Ages

n = 20 Key : 2 4 means 24

How many people in the queue?

How many people in their forties?

20

6

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Stem Leaf GraphsStem Leaf GraphsConstruction of Stem and Leaf

Example : Construct a stem and leaf graph for the following weights in (kgs) :

1 2

2

3

4

5

stem leaves

Weight (kgs)

n = 20 Key : 2 3 means 23

2

1

0

3

3 9

2 2

0 1 1

1 4 5 5

5 5

5 7

1212 4040 5757 5454 5555

1313 5555 1515 3232 5555

3232 1515 4141 2121 4040

2323 4141 2929 5151 1212

1212 1212 1313 1515 1515

2121 2323 2929 3232 3232

4040 4040 4141 4141 5151

5454 5555 5555 5555 5757

We can now answer various questions about

the data.

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2

1

0

3

3 9

2

0 1 1

1 4 5 5

5 5

5 7

2 2

Dot Plot

1 2 3 4

1

2

3

4

5stem leaves

Weight (kgs)

We can convert stem leaf into a simpleDot diagram by taking each level and

adding a dot for each leaf

5

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Charts & TablesCharts & TablesStem Leaf & Dot Diagram

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Explain why the statement below are true or false.

Factorising x2 – 9 we get (x - 3)(x - 3)

Multiply out 4x – 2( 8 – x) = 2x -16

6 14 188 831

7 15 105 105

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1. To construct a Back to Back Stem-Leaf Graph and answer questions based on it.

1. Construct and understand the Key-Points of a Back to Back Stem-Leaf Graph.

Stem Leaf GraphsStem Leaf GraphsConstruction of Back to Back Stem-Leaf

2. Answer questions based on the graph.

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Stem Leaf GraphsStem Leaf GraphsBack to Back Stem – Leaf Graphs

14 0 2 6

15 3 4

16 0 1 6

17 1 6

18 1 4 4

Rugby Team 2Heights

14 | 1 represents 141cm

7 82 1

7 6

4

5 08

3 1346

7 0

n = 15 n = 15

Rugby Team 1Heights

A back to back stem-leaf helps us to compare two

sets of data.

Write down a question that can

be answered easily from the

graph.

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Charts & TablesCharts & TablesBack to Back Stem Leaf Graphs

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2

2 2

1. Find two numbers that add to give -13

an multiply to give - 48.

2. Why does x +8x +15 f actorise to (x + 5) (x + 3)

3. Solve (2x + 8) = 4x .

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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 figure 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

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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

Q2. Find the area of the first shape and the perimeter of the second shape.

(p - 2)

9

(y – 5)

3

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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

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.

5. The boys show less variability in height.

4. The smallest person is a girl

6. The tallest person is a boy

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Box Plot Box Plot

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21. Factorise x +11x+28

2. Explain why 2(x + 5) = x + 12 when x = 2

2 1 133. I s it true that 3 + 2 5

3 5 15

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1. To construct a scattergraph and answer questions based on it.

1. Construct and understand the Key-Points of a scattergraph.

ScattergraphsScattergraphsConstruction of Scattergraphs

2. Know the term positive and negative correlation.

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ScattergraphsScattergraphsConstruction of Scattergraph

Team

100

120

140

160

180

0 20 40 60

Weight (kg)

Hei

ght

(cm

) Sam

Jim

Tim

GaryJoe

Dave

Bob

This scattergraph shows the heights and weights of a

sevens football team

Write down height and weight of each

player.

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xxx x

x x

Strong positive correlation

xx

x xx

x

Strong negative correlation

Best fit line

Best fit line

When two quantities are strongly connected we say there is a strong correlation between them.

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0

2

4

6

8

10

12

0 2 4 6 8 10 12

Ages (Years)

Car

pri

ces

(£1000)


Is therea

correlation?If yes, what

kind?

AgeCar Price(£1000)

3

1

1

2

3

3

4

4

5

9

8

87

6

5

5

4

2

Strong negative correlation

Draw in the best fit line

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ScattergraphsScattergraphsConstruction of Scattergraphs

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