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S3.3 Tables & Charts 11-Jun-14Created by Mr. 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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S3.3 Starter Questions 11-Jun-14Created by Mr. Q1.Does 5x 2 – 16x + 3 factorise to (5x - 1)(x – 3) Q2.Change into £s 75 exchange rate £1 1.5 Q3.Convert to scientific notation

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S Jun-14Created by Mr. Lafferty 3 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.

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11-Jun-144 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 DataTallyFrequency Sum of Tally is the Frequency llll represents a tally of 5

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11-Jun-14Created by Mr. Lafferty5 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 Frequency tables Lowest number56 Highest number62

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11-Jun-14Created by Mr. Lafferty6 DiameterTallyFrequency l l l l l l Frequency tables X X XXXX

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11-Jun-14Created by Mr. Lafferty7 DiameterTallyFrequency Total Frequency Tables lll llll lll llll X X XXXX X X XXXX X X XXXX X X XXXX X X XXXX X X XXXX X X XXXX X X XXXX Relative Frequency R48 3 ÷ 48 = ÷ 48 = ÷ 48 = ÷ 48 = ÷ 48 = ÷ 48 = ÷ 48 = Relative Frequency always adds up to 1 Relative Frequency used with Pie charts

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S Jun-14Created by Mr. Now try Ex 3.1 Q2 Ch6 MIA (page 108) Charts & Tables

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S3.3 Starter Questions Starter Questions 11-Jun-14Created by Mr. Lafferty Maths Dept. Q2.Find the area for the shapes Q3.Write in standard form (w - 2) 7 (x – 5) (x – 3)

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S Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Add a third column to a frequency table to create a Cumulative Frequency Table. 1. To explain how to construct a Cumulative Frequency Table. Cumulative Frequency Tables

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S Jun-14Created by Mr. Lafferty Maths Dept.DayFreq.(f) Example : This table shows the number of eggs laid by a clutch of chickens each day over a seven day period A third column is added to keep a running total (Cumulative Frequency Table). This makes it easier to get the total number of items Cum. Freq. Total so far Cumulative Frequency Tables You have 1 minute to come up with a question you can easily answer from the table.

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S Jun-14Created by Mr. Lafferty Maths Dept. Now try Ex 3.2 Ch6 (page 109) Cumulative Frequency Tables

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S3.3 Starter Questions 11-Jun-14Created by Mr. Q1. Factorise 4x 2 + 9x - 9 Q2. Multiply out (a)a(ab – a)(b)-2a( b 2 – a) Q3.

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S Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 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 Graphs Construction of Stem-Leaf 2. Answer questions based on the graph.

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S Jun-14Created by Mr. Lafferty Maths Dept. Stem Leaf Graphs Construction 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 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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S Jun-14Created by Mr. Lafferty Maths Dept. Stem Leaf Graphs Construction of Stem and Leaf Example : Construct a stem and leaf graph for the following weights in (kgs) : stem leaves Weight (kgs) n = 20 Key : 2 3 means We can now answer various questions about the data.

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S Dot Plot stem leaves Weight (kgs) We can convert stem leaf into a simple Dot diagram by taking each level and adding a dot for each leaf 5

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S Jun-14Created by Mr. Lafferty Maths Dept. Now try Ex 4.1 Ch6 (page 112) Charts & Tables Stem Leaf & Dot Diagram

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S3.3 Starter Questions 11-Jun-14Created by Mr. Explain why the statement below are true or false. Factorising x 2 – 9 we get (x - 3)(x - 3) Multiply out 4x – 2( 8 – x) = 2x -16

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S Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 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 Graphs Construction of Back to Back Stem-Leaf 2. Answer questions based on the graph.

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S Jun-14Created by Mr. Lafferty Maths Dept. Stem Leaf Graphs Back to Back Stem – Leaf Graphs Rugby Team 2 Heights 14 | 1 represents 141cm n = 15 Rugby Team 1 Heights 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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S Jun-14Created by Mr. Lafferty Maths Dept. Now try Ex 4.2 Ch6 (page 113) Charts & Tables Back to Back Stem Leaf Graphs

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S3.3 Starter Questions Starter Questions 11-Jun-14Created by Mr. Lafferty Maths Dept.

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S Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Understand the terms L, H, Q 1, Q 2 and Q To explain the meaning and show how to workout the five figure summary information for a set of data. Five Figure Summary 2.Be able to work L, H, Q 1, Q 2 and Q 3 For a set of data

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S3.3 When a set of numbers are put in ORDER, it can be summarised by quoting five figures. Five Figure Summary 1. The highest number(H) 2. The lowest number(L) 3. The median, the number that halves the list (Q 2 ) 4. The upper quartile, the median of the upper half (Q 3 ) 5. The lower quartile, the median of the lower half (Q 1 )

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S Jun-14Created by Mr. Lafferty Maths Dept. Five Figure Summary Example Find the five figure summary for the data. 2, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10 L = Q 3 = Q 2 = Median (middle value) Q 2 = H = Q 1 = The 11 numbers are already in order ! Q 3 = upper middle value Q 1 = lower middle value

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S Jun-14Created by Mr. Lafferty Maths Dept. Five Figure Summary Example Find the five figure summary for the data. 2, 4, 5, 5, 6, 7, 7, 8, 9, 10 L = Q 3 = Q 2 = Median (middle value) Q 2 = H = Q 1 = The 10 numbers are already in order ! Q 3 = upper middle value Q 1 = lower middle value

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S Jun-14Created by Mr. Lafferty Maths Dept. Five Figure Summary Example Find the five figure summary for the data. 2, 4, 5, 5, 6, 7, 8, 9, 10 L = Q 3 = Q 2 = Median (middle value) Q 2 = H = Q 1 = The 9 numbers are already in order ! Q 3 = upper middle value Q 1 = lower middle value

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S Jun-14Created by Mr. Lafferty Maths Dept. Now try Ex 5.1 Ch6 (page 115) Five Figure Summary

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S3.3 Starter Questions Starter Questions 11-Jun-14Created by Mr. Lafferty Maths Dept. 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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S Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.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. Box Plot

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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 Q1Q1 Upper Quartile = 9 Q3Q3 Median = 8 Q2Q2

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Upper Quartile = 10 Q3Q3 Lower Quartile = 4 Q1Q1 Median = 8 Q2Q2 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 = = 6 Example 2: Find the median and quartiles for the data below.

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Median Lower Quartile Upper Quartile Lowest Value Highest Value Box Whisker Boys Girls cm 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.

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Lower Quartile = 5½ Q1Q1 Upper Quartile = 9 Q3Q3 Median = 8 Q2Q , 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.

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Upper Quartile = 10 Q3Q3 Lower Quartile = 4 Q1Q1 Median = 8 Q2Q2 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

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Upper Quartile = 180 Q3Q3 Lower Quartile = 158 Q1Q1 Median = 171 Q2Q2 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, cm

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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 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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S Jun-14Created by Mr. Lafferty Maths Dept. Now try Ex 6.1 Ch6 (page 117) Box Plot

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S3.3 Starter Questions Starter Questions 11-Jun-14Created by Mr. Lafferty Maths Dept.

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S Jun-14Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.To construct a scattergraph and answer questions based on it. 1.Construct and understand the Key-Points of a scattergraph. Scattergraphs Construction of Scattergraphs 2. Know the term positive and negative correlation.

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S Jun-14Created by Mr. Lafferty Maths Dept. Scattergraphs Construction of Scattergraph Sam Jim Tim Gary Joe 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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S Jun-14Created by Mr. Lafferty Maths Dept. Scattergraphs Construction of Scattergraph x x x x x x Strong positive correlation x x x x x 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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S Jun-14Created by Mr. Lafferty Maths Dept. Scattergraphs Construction of Scattergraph Is there a correlation? If yes, what kind? Age Car Price (£1000) S t r o n g n e g a t i v e c o r r e l a t i o n Draw in the best fit line

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S Jun-14Created by Mr. Lafferty Maths Dept. Now try Ex 7.1 Ch6 (page 120) Scattergraphs Construction of Scattergraphs

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