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S5 Int2

Relative Frequency

Tables Charts & Graphs

Reading Pie Charts

Constructing Pie Charts

Cumulative Frequency Tables

Cumulative Frequency Graphs

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Dot Plots

Five Figure Summary

Box Plots

Created by Mr. Lafferty Maths Dept.

S5 Int2

Starter Questions

- Factorize 3x3 – 9
- A car depreciates at 15% per year. How much is it worth after 3 years, if it cost £12000 initially?
- Write 85% as a common fraction in its simplest form.

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Relative Frequency

S5 Int2

Tables Charts & Graphs

Learning Intention

Success Criteria

- Know the term relative frequency.

- To understand the term relative frequency.

- Calculate relative frequency from data given.

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Relative Frequency always added up to 1

Relative Frequency

S5 Int2

Relative Frequency

How often an event happens compared

to the total number of events.

Tables Charts & Graphs

Example : Wine sold in a shop over one week

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0.5

180 ÷ 360 =

0.25

90 ÷ 360 =

0.25

90 ÷ 360 =

1

360

Created by Mr Lafferty Maths Dept

Relative Frequency

S5 Int2

Relative Frequency

How often an event happens compared to the total number of events.

Tables Charts & Graphs

Example

Calculate the relative frequency for boys and girls

born in the Royal Infirmary hospital in December 2007.

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Relative Frequency adds up to 1

500

1

0.4

0.6

Created by Mr Lafferty Maths Dept

Tables Charts & Graphs

S5 Int2

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.

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Tables Charts & Graphs

S5 Int2

We add the frequencies to get a total

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300

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Tables Charts & Graphs

S5 Int2

Then we work out the fraction of time each sport takes

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Tables Charts & Graphs

Relative Frequency

S5 Int2

Now try Exercise 1

Ch10 (page 138)

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S5 Int2

Starter Questions

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Pie Charts

Reading Pie Charts

S5 Int2

Learning Intention

Success Criteria

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

- 1. To interpret information from Pie Charts.

- 2.Use relative frequency to interpret Pie Chart information.

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Reading Pie Charts

Pie charts can be thought of as circle graphs.

Two step process

- 1.Work out relative frequency of each angle.
- 2. Then multiply by the total amount that the circle represents.

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Tea

Coffee

Tea

72o

Squash

144o

Milk

108o

Coffee

Squash

36o

Milk

Pie Charts

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.

Use the two step process

Created by Mr. Lafferty

Tables Charts & Graphs

Reading Pie Charts

S5 Int2

Now try Exercise 2

Ch10 (page 140)

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S5 Int2

Starter Questions

2cm

3cm

29o

4cm

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A

C

70o

53o

8cm

B

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Pie Charts

Constructing Pie Charts

S5 Int2

Learning Intention

Success Criteria

- Find fractions of 360o.

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

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

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Favourite Sport

Rugby

75

Football

90

Cricket

45

Ice Hockey

60

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.

Relative Frequency

75 ÷ 300 × 360 = 90°

90 ÷ 300 × 360 = 108°

45 ÷ 300 × 360 = 54°

60 ÷ 300 × 360 = 72°

30 ÷ 300 × 360 = 36°

Total

300

Created by Mr. Lafferty Maths Dept.

Drawing Pie Charts

Favourite Sport

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

75

Football

90

Cricket

45

Ice Hockey

60

Squash

30

Total

300

Created by Mr. Lafferty Maths Dept.

Drawing Pie Charts

Favourite Sport

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

75

Football

90

Cricket

45

Ice Hockey

60

Squash

30

Total

300

Rugby

Created by Mr. Lafferty Maths Dept.

Drawing Pie Charts

Favourite Sport

Rugby

75

Football

90

Cricket

45

Ice Hockey

60

Squash

30

Rugby

Total

300

Created by Mr. Lafferty Maths Dept.

Drawing Pie Charts

Favourite Sport

Rugby

75

Football

90

Cricket

45

Ice Hockey

60

Squash

30

Rugby

Total

300

Football

Created by Mr. Lafferty Maths Dept.

Drawing Pie Charts

Favourite Sport

Rugby

75

Football

90

Cricket

45

Ice Hockey

60

Squash

30

Rugby

Football

Total

300

Created by Mr. Lafferty Maths Dept.

Drawing Pie Charts

Favourite Sport

Rugby

75

Football

90

Cricket

45

Ice Hockey

60

Squash

30

Rugby

Football

Total

300

Cricket

Created by Mr. Lafferty Maths Dept.

Drawing Pie Charts

Favourite Sport

Rugby

75

Football

90

Cricket

45

Ice Hockey

60

Squash

30

Rugby

Football

Total

300

Cricket

Created by Mr. Lafferty Maths Dept.

Drawing Pie Charts

Favourite Sport

Rugby

75

Football

90

Cricket

45

Ice Hockey

60

Squash

30

Rugby

Football

Total

300

Cricket

Squash

Ice Hockey

Created by Mr. Lafferty Maths Dept.

Drawing Pie Charts

Favourite Sport

Rugby

75

Football

90

Cricket

45

Ice Hockey

60

Squash

30

Football

Rugby

Total

300

90o

108o

36o

54o

72o

Squash

Cricket

Ice Hockey

Created by Mr. Lafferty Maths Dept.

Worksheet Constructing a Pie Chart

Drawing Pie Charts

FavouriteSport

Rugby

75

Football

90

Cricket

45

Ice Hockey

60

Squash

30

Total

Created by Mr. Lafferty Maths Dept.

Constructing Pie Charts

S5 Int2

Now try Exercise 3

Ch10 (page 141)

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S5 Int2

Starter Questions

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Cumulative Frequency Tables

S5 Int2

Learning Intention

Success Criteria

- Add a third cumulative column to a frequency table.

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

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Cumulative Frequency Tables

S5 Int2

Example : This table shows the number

of cars sold by a motor dealership each

day over a seven day period.

Cum. Freq.

Total so far

1

2

2

A third column is added to keep a

running total. This makes it easier to

get the total number of items.

2

3

5

3

1

6

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

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4

6

12

5

5

17

6

8

25

7

4

29

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Cumulative Frequency Tables

1 minute to come up with a question

S5 Int2

Construct a cumulative frequency table for this data

Shoe Size

1

1

1

4

5

2

5

10

3

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14

24

4

2

26

5

4

30

6

30

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Cumulative Frequency Tables

S5 Int2

Now try Exercise 4

Ch10 (page 143)

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S5 Int2

Starter Questions

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Cumulative Frequency Tables

S5 Int2

Learning Intention

Success Criteria

- Be able to construct a cumulative frequency graph.

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

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How to draw a cumulative frequency graph

S5 Int2

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Plot

How to construct a

Cumulative Frequency Graph

S5 Int2

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Cumulative

Frequency Graphs

S5 Int2

Sometimes called an

S – curve graph

Write down a question you could ask about this graph.

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Cumulative

Frequency Graphs

S5 Int2

Now try Exercise 5

Ch10 (page 145)

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S5 Int2

Starter Questions

10cm

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90o

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Dot Plot

S5 Int2

Learning Intention

Success Criteria

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

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

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

S5 Int2

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Write down as many key points that you can deduce from the plot.

Lowest value is 56 BPM.

Highest value is 74 BPM.

Mode is 62.

Median is also 62.

Distribution is fairly flat.

Dot Plot

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

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50

60

70

80

By looking at the shape of the distribution try and describe the 6 types we have.

Dot Plot

S5 Int2

Common expressions for various dot plots.

Symmetrical distribution

Widely spread out distribution

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Uniform distribution

Tightly clustered distribution

Skewed to the right distribution

Skewed to the left distribution

Dot Plot

S5 Int2

Now try Exercise 6

Ch10 (page 147)

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S5 Int2

Starter Questions

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33o

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Five Figure Summary

S5 Int2

Learning Intention

Success Criteria

- Understand the terms
- L , H, Q1, Q2 and Q3.

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

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- Be able to work
- L , H, Q1, Q2 and Q3
- For 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.

Five Figure Summary

S5 Int2

1. The highest number(H)

2. The lowest number(L)

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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)

Five Figure Summary

Q2 = Median (middle value)

Q1 = lower middle value

S5 Int2

Q3 = upper middle value

Example Find the five figure summary for the data.

2, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10

The 11 numbers are already in order !

5

7

8

Q1 =

Q2 =

Q3 =

5

8

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7

L =

2

H =

10

2

4

5

6

7

7

9

10

Created by Mr. Lafferty Maths Dept.

Five Figure Summary

Q2 = Median (middle value)

Q1 = lower middle value

S5 Int2

Q3 = upper middle value

Example Find the five figure summary for the data.

2, 4, 5, 5, 6, 7, 7, 8, 9, 10

The 10 numbers are already in order !

8

Q1 =

Q2 =

Q3 =

5

6.5

5

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7

7

8

L =

H =

10

2

2

4

5

6

9

10

Created by Mr. Lafferty Maths Dept.

Five Figure Summary

Q2 = Median (middle value)

Q1 = lower middle value

S5 Int2

Q3 = upper middle value

Example Find the five figure summary for the data.

2, 4, 5, 5, 6, 7, 8, 9, 10

The 9 numbers are already in order !

6

8.5

Q1 =

Q2 =

Q3 =

4.5

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5

5

7

8

6

L =

H =

10

2

2

4

9

10

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Five Figure Summary

S5 Int2

Now try Exercise 7

Ch10 (page 150)

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S5 Int2

Starter Questions

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Box Plot

S5 Int2

Learning Intention

Success Criteria

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

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

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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

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

Two middle values so take the mean.

Ordered data

Median drive = 90 yards

Q2

Q1

Q3

Upper Quartile = 9

Lower Quartile = 5½

Median = 8

Finding the median, quartiles and inter-quartile range.

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

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

Order the data

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

Inter- Quartile Range = 9 - 5½ = 3½

Q2

Q3

Q1

Upper Quartile = 10

Lower Quartile = 4

Median = 8

Finding the median, quartiles and inter-quartile range.

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

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

Order the data

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

Inter- Quartile Range = 10 - 4 = 6

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.

Median

Whisker

Whisker

Box

Boys

cm

Girls

130

140

150

160

170

180

190

4

5

6

7

8

9

10

11

12

Lower Quartile

Upper Quartile

Lowest Value

Highest Value

Drawing a Box Plot.

Example 1: Draw a Box plot for the data below

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

Q2

Q1

Q3

Upper Quartile = 9

Lower Quartile = 5½

Median = 8

4

5

6

7

8

9

10

11

12

Drawing a Box Plot.

Example 2: Draw a Box plot for the data below

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

Q2

Q3

Q1

Upper Quartile = 10

Lower Quartile = 4

Median = 8

12

13

3

4

5

6

7

8

9

10

11

14

15

Drawing a Box Plot.

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

Q2

Q3

Q1

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

Upper Quartile = 180

Lower Quartile = 158

Median = 171

130

140

150

160

170

180

cm

190

Drawing a Box Plot.

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.

Boys

cm

Girls

1.The girls are taller on average.

2.The boys are taller on average.

130

140

150

160

170

180

190

3.The girls show less variability in height.

5.The smallest person is a girl

4.The boys show less variability in height.

6.The tallest person is a boy

Box Plot

S5 Int2

Now try Ex 8 & 9

Ch10 (page 152)

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Created by Mr. Lafferty Maths Dept.